The sea change has helped them grow as a couple, Asplund said.

"It puts more strain on the family as a whole when you're not able to share the responsibility of everything," she says. "Now, we both work, we both take care of the kids, we both take care of the house, there's not that rift or division. It was just a lot better."

Children spending more quality time with their fathers has a cascade of social benefits, according to the Swedish government, but it also allows women to pursue their careers and become more active members of the workforce.

In this sense, gender equality is a dispassionate economic goal; right now half of the population is unable to contribute as much as the other because of traditional family commitments.

Some conservative critics say this focus on dads means moms are pressured to abandon their children too soon. The Swedish government disagrees.

"One of the main discussions now is how do we make dads stay at home more," says Harju, the health ministry spokesman. "We are in firm belief that children have the right to spend time with both their parents, and we have to ensure that the system also covers that and pushes society toward that direction."

Another American father with experience in both worlds is Michael Wells, a Minnesota native and an expert on parental leave.

He moved to Sweden to study the country's unique parenting model but ended up meeting a Swedish woman, getting married and having a son.

Michael Wells with his son. Vladimir Banic / for NBC News

"When I originally came, I came to study it, not to live it," says Wells, who works as a researcher at the Karolinska Institute, a medical university in Stockholm.

For Wells, it's not just the family leave that sets Sweden apart but the raft of other social welfare benefits.

For example, parents don't have to take all of their 480 days at once. Some of that time can be deferred up until the child is 12 years old. In addition, the government pays every couple — whether they are janitors or CEOs — an allowance that equates to around $130 per child per month.

Swedes also get a whopping 120 days of "child sick leave" per year, when they can stay home if a child is ill without eating into their own already generous allowance.

"I think Americans would be really surprised by the system here," Wells says. "And the U.S. system would be unfathomable to a Swede."

How does Sweden pay for this? Part of the answer, very broadly, is that Swedes are prepared to pay more in taxes than Americans — much more.

If Sweden's tax system was applied in the U.S., everyone earning more than $75,000 would have to pay the top marginal tax rate of around 61 percent — one of the highest in the world. Currently, only Americans earning around $400,000 hit the top tax bracket of around 46 percent, according to the Tax Foundation, a Washington think tank.

Many in the U.S. might argue this goes against the American spirit distilled by President Ronald Reagan's farewell address in 1989: "We the people tell the government what to do; it doesn't tell us."

At 61 percent, Sweden has one of the highest top marginal tax rates in the world. Bing Maps

But like many in Sweden, Wells says he is happy to pay extra because of the parental leave, subsidized health care, subsidized preschools and a slew of other benefits he gets in return.

"I get a lot from my taxes. I see what they provide," he says. "And as soon as you start having kids, you see all these other benefits that you get out of your taxes that I know I would have to pay for out of my own pocket in the U.S. That's a huge burden off my shoulders."

The Swedish government is now trying to modernize its family leave and update a policy that was devised in the 1970s so it better suits life in 2018.

"For instance, in the LGBT community, where two lesbians or gay people have kids together, how are they able to use the insurance in a sensible way so it's adjusted to different families?" says Harju at the health ministry.

Reid and Wells say they've already encountered an array of reactions from people in the U.S.

"We have a lot of friends who have kids and they all are pretty much asking: 'How do we get to Sweden? How do we live there?'" Reid says.

Asplund has had a different experience. "Yeah, they think it's all communist," she laughs.

Others might argue that the Swedish model — catering to a far more homogeneous population of 10 million than America's 326 million — could never work in the U.S.

Wells disagrees.

"If every other industrialized country in the world can have parental leave," he says, "I'm pretty sure the U.S. can manage to do it, too."

CORRECTION (April 4, 2018, 1:55 p.m. ET): An earlier version of this article misstated the company that Agnes Asplund works for. She works for Rapid Images, a marketing firm whose main client is Volvo — not Volvo itself.