I didn’t have many positive images of working mothers when I was growing up in New York in the 1980s. Ferris Bueller’s estate agent mother was the first one I remember taking notice of, and what I noticed was that she was constantly being reprimanded by authority figures for being a slack parent while Mr Bueller was left alone in his high-tower office, bothered by neither his children’s irate headmaster nor the local police, so he could get on with his day of having fancy lunches. Then there was JC, the Wall Street executive in 1987’s Baby Boom, played by Diane Keaton, whose bosses were so horrified when she became a mother that they basically pushed her out the door. (Banished to Vermont, JC made money the only way open to mothers, which was making baby food.) Probably the best was Clair Huxtable, the lawyer mother in The Cosby Show. But let’s be honest, she never seemed to do much lawyering and, let’s be even more honest, if your most positive example comes from The Cosby Show, then you’re really scraping the barrel.

Like the majority of mothers in Britain, I work. My mother stopped working when I was born and I loved that she was always there when I got home from school – but that is not a financial possibility for me and, anyway, I really like my job. According to the Office for National Statistics, the number of working mothers in England has gone up by more than a million in the past two decades, which means there’s a lot of us who grew up without a roadmap for how to do this. And that can feel at times a little like getting dressed without a mirror.

So when Guardian contributor Fiona Freund asked if she could photograph me with my kids for an exhibition to celebrate working mothers in recognition of International Women’s Day, I said yes. Normally I’d rather eat my own hands than be in front of a camera but I was curious about what I looked like, working and mothering, and when I looked at the photo I saw the prosaic truth: I looked busy, and I looked happy.

You don’t need to come over all Andrea “as a MOTHER” Leadsom to say that you learn a lot about yourself when you combine work and motherhood. What I have mainly learned is that the stereotypes I feared most aren’t true. My brain hasn’t become a baby-centric pudding – in fact, since I had my twins, I’ve never been so full of ideas. Where once I could turn dicking around into an Olympic sport, I can now knock off two articles by lunchtime. One of my friends said she’d become a much better boss since having kids “because I’m used to having to spell things out to the kids all the time”. Also, contrary to all the stories about the guilt working mothers feel, I appreciate my job more than ever, because nothing makes the office feel more like a relaxing holiday than having two toddlers at home. And I will always believe that whatever negligible effect my occasional absence has on my boys, this is more than compensated for by the benefits they get from seeing an ambitious and professionally satisfied woman as the norm.

But some stereotypes remain all too true. My partner and I are both journalists and the only way we could be more professionally equal is if we were the same person. And yet I’m still seen by others as the caretaker: I’m the one the doctor calls if something is wrong and I’m the one who other parents contact to make playdates (and by “other parents” I inevitably mean “other working mothers”). If my boys ever skip school, Ferris Bueller-style, I’ll be the one the headmaster calls, even though I work in an office and my partner works from home.

I emailed my female friends who also have kids and work, and asked how they see their situations, and my inbox filled with mixed emotions, and not just of the busy/happy variety. They felt “lucky” but also “furious”, “good” but also “often crying”. My friends spoke of husbands who get irritable about doing the “childcare” (aka parenting) and male bosses grumbling about their female employees leaving work early for the school pick-up. “I have kids and I work full-time,” one boss crossly told a friend of mine who asked to have Fridays off. “Yes, and your wife quit her job to look after the kids,” my friend couldn’t quite bring herself to reply. Working mothers are becoming the norm, but residuals of the old patriarchy remain – in office practices and also in relationship dynamics.

So here’s my wish for the next International Women’s Day: as well as exhibitions about working mothers, there will be ones depicting fathers doing the school run; male bosses will write articles about the long-term benefits of accommodating women so devoted to their jobs they return to them after giving birth; and no one will take it as a given that it’s the mother who goes part-time after having kids. Because I love the photo of me with my boys, I really do. But if we’re talking about working mothers without looking at the role men have to play, we’re seeing only half the picture.