When I began interviewing fathers all over the country, I discovered that the same thing kept happening. They gave me some permutation of this line: “I’m not like most dads—I’m really involved in my kids’ lives.”

In each case, I asked them to think about the other dads they know. “Do you know any who aren’t like you? Any who ignore their children?” They’d think about it, and say no, adding, “But they’re like me—they’re the exceptions.”

No, they’re not. There’s a huge gap between what dads are actually like these days and what stereotypes and inaccurate reports suggest. Sadly, the stereotypes in TV shows like The Simpsons and Family Guy and all sorts of ads have permeated the American psyche. It’s not just a problem for the U.S. In a survey, British women slammed negative depictions of dads in ads, saying that in reality their partner is equally involved in parenting.

This Father’s Day, let’s take a moment to see what’s really going on with modern dads.

For starters, they’re not lazy, and don’t sit around the house doing nothing. Overall, fathers and mothers work equally hard on behalf of their families. The American Time Use Survey collects data on activities in tens of thousands of homes. Dads put in an average of 54 hours a week, and moms put in 53. (Factor in room for standard errors and you’ve got basically a tie.)

A lot of the confusion surrounding this is that there’s a big difference in how that work is distributed. “Work” includes paid work, unpaid work (such as household chores) and childcare. Dads on average put in more hours at the office, and moms put in more hours at home. Some reports ignore paid work hours and focus only on household work and childcare, assailing dads for doing less. They leave the impression that men are relaxing, when they’re actually working to provide.

The same study, the ATUS, also looks at “leisure” and “personal care,” which includes sleep. On this front, dads and moms are also equal. Dads spend a bit more time on “leisure and sports,” while moms spend a bit more time on “personal care.” The combined figures are just about as close to equal as you can get. (12.96 hours a day for dads, 12.99 for moms—a statistical tie.) Again, some reports have misrepresented dads by focusing only on leisure time while ignoring personal care.

And this isn’t just the case in the United States. The Organization for Economic Cooperation and Development says “time devoted to leisure is roughly the same for men and women across the 20 OECD countries studied.”

Also unlike the stereotypes, dads aren’t shirking their children. The average working father spends three hours each workday caring for his children, the Families and Work Institute has found. A CDC study found that virtually all dads who live with their children care for them in every major category at least several days a week if not every day. Those categories include feeding, bathing, doing homework with them, and more. (Among these men, black fathers are actually the most involved. In an interview for my book All In, the lead researcher told me it marks “the debunking of the black-fathers-being-absent myth.”)

The big difference is that dads and moms are spending their working hours differently. That’s because of sexism in how the workplace was designed. Our modern work structures—laws, policies, and stigmas—were created in the Mad Men era. The presumption was that women will always stay home with babies, while men will always make the money.

This explains why the United States remains alone in the developed world for having no paid maternity leave. The thinking behind it was, “She’s a woman, so she doesn’t need to make money. The man should make all the money.”

To this day, the workplace acts as gender police, pushing women to stay home and pushing men to stay at work. Less than one-in-five companies offer any paternity leave. When men try to take that leave or seek flexible schedules, they’re often punished, a series of studies by the Center for WorkLife Law found. All In contains stories of men who were fired, demoted, or lost job opportunities for straying from an outdated, “macho” norm.

The Boston College Center for Work and Family makes this same point in a new report. While taking time for caregiving “can be career limiting for women, it may be even more problematic for men who do not fit the image of the hegemonic male,” it says. The report finds that the vast majority of working fathers and mothers want more time at home with their families, even as they want to advance at work. And EY found that U.S. men are even more likely than women to “change jobs or give up a promotion for work-life management.”

Much of my work these days is with women’s organizations around the country, including those inside many companies. When I present all this information, many participants tell me it comes as a paradigm shift, leading them to recalibrate their understandings of the balance of responsibilities at home -- and to realize how much strain their husbands may be under as well.

Dads are under enormous pressure, and feeling the stress. The American Psychological Association found that overall, stress levels are close between men and women. The University of Michigan found that men’s stress is more likely to lead to depression, partly because men are less likely to talk about their problems and get help.

But as long as people believe dads are living relatively care-free, relaxing lives, we as a society won’t be attuned to these struggles. They’ll remain in the shadows.

This Father’s Day, let’s shine a light on just how well dads are doing. Let’s resolve to work together, men and women, to eradicate the backward structures holding us back. And let’s do what it takes to build a future in which our children have the chance to experience real equality—both at work and at home.