Kordale Lewis has just returned from a late-night visit to the shops with his daughters, Desmiray, 11, and Maliyah, 10. Their large, grandly furnished home in the Atlanta suburbs is humming with anticipation of an imminent family trip to Paris. The girls have bought some accessories and Kaleb Anthony, Kordale’s partner, is taking an inventory.

“What did you dress them in?” he asks. Kordale replies that he bought pink trousers to go with Maliyah’s black flats and grey sweater. Kaleb is dubious: “Black flats with light colours?” Kordale ignores the provocation. “Desmiray is wearing black leggings with that sweater and her brown heels,” he says.

Two black gay men clowning around with their kids is still an arresting image in 2017 as it’s so rarely shown

Another grimace from Kaleb. “Black on top of brown?” Behind us, Desmiray is practising a model’s snaking walk in her heels. Her fathers enrolled her in the Barbizon modelling school and have high hopes for her future career. She and Maliyah recently received video cameras in order to blog their journey into adolescence, and trailed one another around the Target store recording stray observations. This is a household profoundly comfortable with the social-media age.

Neither Kordale nor Kaleb have been to Europe – and this will be no ordinary family vacation. The two men and their four children are attending Paris Fashion Week as guests of Acne Studios – the avant-garde, often precious, Swedish brand that cast the family as the face of its latest campaign after spotting them on Instagram. The Acne images were shot by fashion faves Inez & Vinoodh, who have also photographed Lady Gaga and Barack Obama, among others.

One shot shows the family in the master bedroom, Kaleb resting on the bed, shirt pulled up around his neck to reveal his buff chest and tattoos, while Kordale stands in the foreground, balancing their youngest child, now aged one, on his shoulder. Their three other children, Desmiray, Maliyah, and Kordale Jr, nine, pose and pirouette on the bed behind Kaleb. It is not their first advertising campaign – in 2015 they were in a popular digital video for Nikon cameras– and the couple are determined to make sure it won’t be their last.

Facebook Twitter Pinterest Stars and stripes: the ad campaign for Acne Studios, after which Kordale and Kaleb attended Paris Fashion Week. Photograph: Inez Vinodh/Acne

Were they a straight white family, no one would bat an eyelid, but two black gay men clowning around with their kids is still an arresting image in 2017, because it is so rarely represented in our culture. When Kordale and Kaleb casually posted a selfie to Instagram in January 2014, in which they captured a morning ritual of brushing their daughters’ hair for school, they created the kind of viral moment that advertisers spend tens of thousands of dollars concocting, often without result. And while comments on Twitter and Instagram were not all positive, many others were.

At a time when Black Lives Matter was illuminating a seemingly unending epidemic of police killings of unarmed black men, an image of black gay fathers in a tender moment with their daughters had a particularly poignant resonance.

I knew I’d never be as great as I could be as the police are designed to oppress minorities

The fact that a family selfie on Instagram was noticed at all simply demonstrated how rare such images are in a culture in which black men are routinely demonised as threats to, rather than emblems of, the American family.

It was no bad thing that Kordale and Kaleb were also easy on the eye, and looked like fathers who knew how to enjoy one another’s company after the lights were out. The photo garnered more than 54,000 likes, and has been followed by a steady stream of typical family portraits that show them celebrating birthdays and holidays as well as the birth, last October, of Caleb IV, the latest edition to the family.

Today, KordalenKaleb (to use their Instagram handle) are sitting in their spacious kitchen sharing pizzas with the kids. A dog runs around, alert to the heightened energy as Kaleb preps his hookah with Mojito-flavoured tobacco and Kordale fiddles over the filters for an Instagram selfie.

Yet, against the upbeat fairy tale of the couple’s social media, the story that Kordale tells of his childhood is a cold-water bath of reality, one that makes his success as a father all the more affecting. And it helps illuminate the love and energy and sheer tenaciousness that he’s invested with Kaleb in building a home for their children.

Facebook Twitter Pinterest Crowning glory: Kordale, left, helps Maliyah with her hair as Kaleb, right, helps Desmiray. Photograph: Raymond McCrea Jones/The Observer

“You don’t look at your life as something interesting until other people tell you it’s interesting,” says Kordale, as he recounts his fractured childhood. “I just thought that I was going through shit and I would tell myself: ‘This will all be over one day,’ and keep on going.’”

The “shit” he refers to was his drug-addicted mother and a series of foster homes culminating in a suicide attempt at 13. Through his teens he was in jail more often than he can count, usually for violating probation – which can mean anything from possessing pot to riding on a stolen street sweeper, as he once did for a lark.

These are things white boys do with impunity, but in Dubuque, Iowa, where he reunited with his mother when he was 15, the cops only targeted black men.

“I knew I’d never be as great as I could be,” he says, “because the police were designed to oppress people in that town, bothering minorities all the time, finding any reason to lock them up, and once they found a reason to indict them for a small infraction they were going to send ’em to prison.”

After being expelled from school for beating up a classmate who called him the N-word, Kordale found himself at an alternative high school for expelled students, “high as hell” on Adderall (a drug used to treat ADHD) and sleeping around with girls because that was what a young man was supposed to do. He met Destany Marie Davidson, the mother of his children, in a nightclub at 15.

“Her younger sister was trying to talk to me,” he remembers, “but her older sister came up and said: ‘You should talk to my other sister, she’s prettier than this one.’ And I’m, like: ‘OK, sure.’”

A year later Destany gave birth to Desmiray, and Kordale had to turn his straight role-play into something more serious. “I always knew I was gay, I knew I liked men,” he says. “I just repressed it. It was just too scary a thought to act on it in a small town.”

Facebook Twitter Pinterest High scores: Kaleb helps Desmiray with homework. Photograph: Raymond McCrea Jones/The Observer

Kordale and Destany had two more children in quick succession before it was clear something was wrong. “Before Kordale was born, I was telling her: ‘I want you to try this on me sexually,’ and she was, like: ‘Ugh, that’s so nasty, so gay,’ this and that.’” He pauses. “You really going to put that in the article?” He laughs. “I don’t really care,” he says. “Let me tell you something – sex is tangible to everybody.”

As we talk, in the descending gloom of the evening, Kordale lowers his voice when the children approach, or when he pauses and checks on Desmiray’s grades (“Is this 100? Look at you! Keep practising – get straight As”) or to pacify Caleb IV who is entering a noisy stage. Although there are photos of his mother and father around in the house, he is not yet ready to tell the children why they never get to see their grandfather.

Kordale was 13 when his aunt, in a fit of pique, told him that he was the son of a double-murderer, prompting his suicide attempt. He pulls up a website on his laptop to show a photo of his father face-forward and in profile, above a prisoner number. Suddenly, the happy family he has created takes on a different hue, and is an even more profound achievement.

“I want to know the story of who my daddy killed, why he killed them, and when and where, because I want to reach out to the families and offer an apology,” he says. “I’ve seen mothers bury their kids – it hurts, it’s painful. The idea that someone so close to me, who I’ve never really met, did that, you know?” He trails off. “I’m the type of son that would turn him in, because if something like that happened to me, I’d want the same respect from the family.”

Kaleb was studying engineering at Jackson State University, in Mississippi, when he sent a Facebook message to Kordale in 2009. Having separated from Destany a few years earlier, Kordale was living in Atlanta, figuring out what he really wanted. The two were a match of opposites. Kaleb, from a close-knit family, represented the picket-fence fantasy that Kordale had long pined for. Each week for six weeks, he drove the 380 miles from Jackson to Atlanta so they could be together. Before long, Kordale moved up to Jackson to live with Kaleb.

Facebook Twitter Pinterest Top scores: the family sets up in the kitchen to do homework together after getting home from school. Photograph: Raymond McCrea Jones/The Observer

“Kordale is the reason I’m out,” Kaleb recalls. “It was Christmas, and he’d been telling me he was going home, and I said: ‘What about Christmas?’ and he was, like: ‘That’s just another day.’”

Kaleb insisted he stay with him for the holiday. When his father visited and began questioning the bedroom arrangements, Kaleb floundered until Kordale stepped forward. “Kordale blurted out: ‘Before you ask any more questions, your son has something to tell you,’ so that’s when I told my parents. My dad was like: ‘I’m kind of disappointed,’ and I thought, ‘OK, here we go – he’s one of those dads who doesn’t like gay people,’ and then he said: ‘I just thought we were a lot closer and that you could have come and talked to me about this.’”

They are an idealised version of the America that has been so forcefully repudiated by Donald Trump

It would be disingenuous to say it’s been happy families ever since. There was a brief split in 2015, but the two are sanguine about the challenges and aware they can’t get too caught up in the whirlwind of celebrity that has turned them into a glossy emblem of black gay families. They are an idealised version of the America so forcefully repudiated by Donald Trump, but they are also a repudiation of his America, a manifestation of the better America the country has the potential to be.

As they escort me around their house with its baroque decor, inspired, Kordale says, by The Real Housewives of Atlanta, there is pride in the home they’ve built, the ensuite bathrooms, the flat-screen TVs. It’s easy to scoff at these material trappings of success, but what better rebuke to those who find the idea of a black queer family anathema?

“A lot of people I come across don’t agree with it,” says Destany, who moved to Atlanta three years ago, and now visits the house most nights, and takes the children at weekends. “They say: ‘How do you let your kids move in with two men?”

In an unusual arrangement, Caleb IV is the child of Destany and Kaleb, a production that neither found particularly easy. Kaleb describes a functional exercise in which he would masturbate in the bathroom and then run into the bedroom at the necessary moment, while Destany lay waiting with a pillow over her face. “Having sex with Destany was so strange because she was, like, my best friend,” he recalls. But it was also practical. The two men couldn’t afford adoption or surrogacy, and Destany was already deeply enmeshed in the life of the family. “Our children are just like any other children, but have something a little bit better – a mom and two dads,” says Kaleb. “We all have a 33⅓ take on how these children are raised.”

Does Destany harbour any regrets about sharing custody of her children? “Sometimes I do,” she says. “Sometimes I feel like all my kids should be at home with me, but that’s just a mother’s feeling. They wouldn’t understand.”

“I understand it,” interjects Kaleb softly.

“I don’t,” says Kordale, with stubborn mischievousness.

What about living together: Destany and Kordale and Kaleb? Maybe they can change the Instagram to KordalenKalebnDestany. They all shriek in unison. “Hell, no!” says Destany and Kordale, before Kaleb – the peacemaker here – suggests that to work they’d need to build a second house for Destany and live on several acres. But for that, they may need another advertising gig.

Kordale has already mapped it out. “I picture our family doing a Lexus commercial around Christmas time, with our son who will be fully walking by then – maybe the dog. He’s all groomed up and snow’s falling, things like that,” he says. Kaleb adds: “Wouldn’t that be so hot if our whole family were getting out of a LX 570, 2019 model?”

Kordale, who has built his life through grit and determination, knows they have a powerful brand. “That will be a viral moment for Lexus, I’m telling you,” he says. “If it was any other family,” he says, “it will just be another commercial. I hate to say it, but it’s the truth – I feel we have the spark, for whatever reason.” Kaleb nods, and says: “We need to get us an agent.”