Wow, this thread. Hope you two are able to have some productive discussions on this topic in private.
The larger topic of household/parental responsibilities in hetero relationships is an interesting one. I personally (as a woman) am wildly concerned about maintaining an equal labor divide with my husband when kids are in the mix. (And yes, we discuss this frequently.) I find the cultural dialogue around parenting to be really problematic (women's most meaningful role is as mothers, men are incompetent at caring for their own children, ick to both). Some study I read recently showed that expectations pre-parenting are that things will be more equal than they end up being (with people reverting to more traditional roles). This thread prompted my talking to my husband about whether I was being sexist by having him pull our suitcase while we were traveling. (He's clearly stronger than me ... but we're clearly both strong enough to pull a suitcase, and there's no reason why I should expect him to do it.) I want him to point out to me when I do stuff like this. I made it a point to pull the suitcase for the rest of the trip.
I think it's important to realize that it's not always easy to be compassionate and egalitarian and look out for your partner's needs equally to your own ... and times of stress (which parenting certainly entails) only make it harder. If your husband isn't acting in a way that fits both of your preferences for HH duty allocation ... it's very unlikely he'll change and do more work after kids. I'm waiting a while to have a kid (and only want one) because it's a huge concern of mine that I'll bear the brunt of the work, and our division will be unequal, which would be very bad and unhappy for me. And this is all while having an amazing partner who is objectively better at cleaning and cooking than me, who is a feminist and very much enjoys kids, and with a division of labor that is currently equal. (It really helps to have a minimalist apartment/not a lot of stuff, so there's not much cleaning to do generally.)
Some thoughts (from my own experience and elsewhere) on how to be equals in your relationship and HH duties, if that's what you strive for:
1) As said above - minimize the HH labor needed, period. Declutter, donate stuff, keep things more minimal, and there's less to clean.
2) Divide some tasks completely: ie, I do EVERYTHING with finances (bills, taxes, CCs, travel hacking, tracking spending, investing), and he does everything with the car (we have one car, it was originally his). So we don't ever argue about who does these tasks.
3) Take on tasks strategically: Only I get our mail because it would drive me crazy for him to leave junk mail and not throw it out right away. So I take on the task, because it's better if I just do it.
4) Agree to some schemas: For us, if one person cooks dinner, the other does the dishes. We both agree that's fair. This excludes when he cooks a huge batch of food because he's super messy and uses way more dishes than needed and doesn't clean up along the way, like me. But we generally keep to it.
5) It's ok to pass on labor-intensive things that only your partner cares about. For example, while I love meat, I eat pretty vegetarian at home and love to have soups and salads. My husband wants meat more often, so he'll be the one to make pork roasts and lamb etc that we have frozen in our freezer from Costco. I see this as helping us stay at an equitable equilibrium. I do cook meat too, but when he wants it more often, the onus is on him to make it (which he happily does).
6) Try to be helpful and charitable to your partner - if you're seeing large imbalance over time, definitely talk. But I find that not keeping score and trying to do nice things for my partner leads to him doing the same (ie, this morning I woke up to see he'd done all the dishes before going to work and made me a lunch). You may feel you are doing more - be mindful and remember everything he does for you.