I probably should also mention, not having read all the other contributions, that although I was the one who tended to organise childcare, extra curriculars, buying uniform, meal planning, diary organisation, groceries and other shopping etc, it was by no means a foregone conclusion that I would and plenty of jobs were fairly shared.
DH would drop DD to creche in the mornings (commuting by bike) and I would collect in the evenings (collecting by car until 2.5, and by public transport until primary school, then it had to go back to car for logistical reasons). DH would also often do the morning drop at school when he was at home (he was away 50% of the time for work in the lower 4 years of primary, so an au pair helped a lot at that stage).
If DD was sick, we would jointly look at our diaries and juggle who had the greatest needs at what times, mostly we managed to do it by 1 doing a very early morning start, swopping at lunchtime, and the other staying later than usual, and both catching up in the evening at home. But being flexible about what meetings couldn't be cancelled or moved for each other.
Yes, I did most of the PT meetings (DH did a lot with me, but not always), and almost inevitably was solo at the shows, events, presentations etc in school if I could get there. But DH brings her to training, and matches, almost every weekend. And spends hours on end out the front doing extra training with her. And video analysis and other things with her.
While I've been the main one to do training for ASD, we both did the parenting course, and he has actively listened when I have told him things I've learned. We have developed plans and strategies together (I may have done a lot of research before talking to him, but sometimes he will have too, and we agree the strategy before implementing anything) and while there might be some slight difference in how we approach things, we are working together and are able to give the same messages to DD.
And DH is actually far more likely than me to do housework on a daily basis. In recent years, the split has moved from either doing anything that's needed, to more like I'll cook and he'll washup (although he is a decent cook), he does laundry (including all ironing since DD was born and he couldn't feed her) but I will sort a load if up earlier to do it and hang out plenty on the line. We have different skills in DIY - I'm great at preparing for painting but leave streaks, whereas DH is slapdash preparing but great at the painting, he tiles while I grout, I'll tackle most emergencies and have the contacts to call in tradespeople if needed, but DH would tend to do more of the regular maintenance and putting together things (although I am the one who tends to deal with blocked pipes and gutters....as I will do a pro-active check (and cleaning) regularly whereas DH will leave it til there's a problem).
And he is happy to share driving too - whether on long or short journeys, and whether in his car or mine.
It might not be entirely equal in everything, but it is a fair balance on the whole.