A father and mother are still typically presented as the desirable norm for family life: usually portrayed laughing along with a couple of smiling, cherubic offspring. But families come in all shapes and sizes. There are more than two million one-parent households in the UK, and approximately 8,000 families comprising same-sex parents with children, according to the Office for National Statistics. If such families are occasionally now being depicted in the media (the pushchair company Mamas & Papas broke new ground in October when it used an image of a gay male couple in an advertising campaign), the visibility of households with children with disabilities remains low.

This all makes the Hastings household presided over by David Upjohn and Andrew Daniels somewhat unusual. David, 59, and Andrew, 47, are foster carers and have also been adoptive parents.

They have been together in a relationship for 24 years, and before they became full-time carers, Andrew taught at a school for children with special needs, and David worked in adult social care.

They first fostered 18 years ago. Then, the idea of two men adopting a child was uncommon, which is partly what led them to foster when, due to Andrew's experience with children with special needs, they were asked if they would look after a boy with severe disabilities. "He wasn't expected to live to his first birthday, although he eventually lived until he was seven and a half," says Andrew.

The death of a child will always be traumatic, but Andrew and David felt compelled to continue.

"He'd taught us so much and we'd developed so many skills … we thought, we can't just leave it. We've got to do something with this knowledge. That's when we decided to carry on fostering children with profound disabilities and terminal conditions."

The couple contacted Credo Care, an organisation that specialises in disability foster placements. Shortly after, Armand arrived.

"He arrived in March, 10 years ago," explains David. Born in the Democratic Republic of the Congo, six-year-old Armand had lived in hospital for most of his short life. A wheelchair user, he has severe learning disabilities, a tracheotomy and is fed through a Peg [percutaneous endoscopic gastrostomy].

"He came to us when he was six and was the first one to arrive. Four months later, we had an emergency phone call, asking us if we'd take a boy from Derby. Luke arrived that afternoon. He was 12 and had Duchenne muscular dystrophy. In those days he could shuffle around, but now, he's totally … well, the disease has got hold of his body. He's 22 now. He's a great lad, he really is. He's brilliant."

A couple of months after Luke joined the household, the couple were asked to take Steven, who was five and had cerebral palsy and learning difficulties. They have looked after the three boys ever since. Two years ago, they adopted a little girl. Sadly, she wasn't well and didn't live long.

"We had 17 wonderful months," says David. "She was three when she died. It was just 10 days after the adoption was completed, and it was very sudden, so … we haven't gone down that road again," he adds, choosing his words carefully to describe what must have been a devastating experience.

The latest addition to the household arrived earlier this year. Three-year-old Emma is immobile, has limited vision and breathes via a tracheotomy, but appears to be thriving in their care.

"She's making huge progress," says Andrew. "She was in a place in Surrey, where she had lots of different people working with her. She couldn't make connections with people. Now she just has two voices that she hears all the time – the same people caring for her. And we have the luxury of spending time with her."

Talking to David and Andrew, I am struck by how matter-of-factly they talk about their family setup. They clearly derive great joy and reward from their role as carers, speaking about each child with affection and deep pride. To an unexperienced outsider, the idea of caring full-time for a child with severe learning difficulties – who may not be expected to live until adulthood – probably falls into the category of every parent's worst nightmare. However, the couple are a testament to the fact that it doesn't have to be regarded that way.

"I love every minute of it. It really is wonderful to watch the children grow and develop," says David. "Maybe sometimes you're just looking for them to smile because the milestones are not the same as other families – where they start walking, they start feeding themselves, they get toilet-trained … we have none of that. We get excited when they smile and recognise us. Or maybe they turn their head at the appropriate moment. That's a huge milestone for our children."

Have they experienced prejudice, either towards their children or as a gay couple? "People are surprised," says David, carefully.

"Actual, outright homophobia? No. When you're out with four children along the seafront, people do stare at you. Quite often young children will come across and look and we encourage them to talk to the children."

"We have four children who use wheelchairs. We're quite a presence," says Andrew, laughing. "If we walk along the street, you tend to notice us!"

"The worst incident was a man walking along the pavement staring at the boys so much that he walked straight into a lamp-post," says David. "I suppose," he adds mischievously, "I could have stopped him …"

"There hasn't been in-your-face homophobia," adds Andrew, "but in the early days there were a number of children that we were likely to foster, and nothing happened. Then we found out later that a parent had said, 'No, they're not going there' – but that was a long time ago.

"More recently, a child was placed with us this March, but her father was very against it. He initially said, 'No, I don't want her going there, I don't want two male carers.'

"There were also issues about her being so far away from where he lived. But he's comfortably on board now, and he visits. You get little comments. Like when I first met him, I answered the door and he said, 'Which one are you, David or Elton?'

"But I think he's on quite a learning curve, actually, because he said, 'You know, when she first came here, I thought she was going to be dressed in dungarees and have her hair cut short, and things like that.'

"So," he adds diplomatically, "some quite powerful stereotypes going on there."

This example illustrates one of the biggest differences between adoption and fostering. While an adopted child is likely to have no contact with their biological parents, parental contact with foster children is more common. Social services and fostering organisations will also have a far greater input into the children's care as, ultimately, the child's welfare remains the responsibility of such organisations. Foster carers are also paid – enough so that David and Andrew gave up their full-time jobs – but it's certainly not something you would do for financial gain.

Fostering can also be a temporary measure, offering respite to parents who are unable, for whatever reason, to cope or adequately look after their child. David and Andrew's children are long-term commitments, although, given the nature of their disabilities, how long can be hard to predict. It's a sobering moment when Andrew says, "Our eldest boy has a terminal condition: Duchenne muscular dystrophy. He's already four years past the age at which we expected him to no longer be with us, so we have quite a few medical issues with his respiratory health – he gets more chest infections. But he's incredibly happy. He has a mild learning difficulty, but he's lovely. Really lovely."

I am left amazed by David and Andrew. Despite the challenges, their lives are full of rewards. Their love for and pride in their children is obvious. What advice would they give to anyone thinking of fostering?

"I would say find what area of fostering that you want to go in," says David. "Disabilities isn't for everyone. For example, if you were to tell me that I was to have a child with autism, that wouldn't suit me at all ... or challenging needs where perhaps they can be quite vicious and spiteful. I couldn't cope with that. But then there are other people – gay couples we know – who are doing that and who are doing a wonderful job. So it's about finding out what's right for you. Having found that, I think it's the most rewarding thing on this earth."

Andrew adds: "Because of the terminal conditions of our children, I think we've developed this idea that none of us know how long we're going to be here, so we should make it as amazing as possible," adds Andrew.

"I think that feeds into our lives as well. It gives life an amazing quality. It digs deep into a part of you that you didn't know was there. It's sometimes incredibly painful. You sometimes think, 'I'm not sure I could face that again.' But you do. You engage with the child and, again, that ethos of quality before quantity comes out.

"It's not like the cover of a magazine where everyone is smiling. It can be challenging, but you learn new skills to deal with those things. But, overall, it's one of the most life-enhancing experiences you could ever have."

• Some of the children's names have been changed. This article first appeared in Out In The City, outmag.co.uk. For more information on fostering children with disabilities, go to credocare.co.uk