Before I read your update I was going to say that yes it's ok to expect more, evened out over time
However if your children are very young then I think no one can really expect anything, we certainly found that they were cranky in the evenings and things like cooking where you can't easily do it while holding a child and they wont be put down, were very difficult when they were under 18 months.
It's also something that happens organically and evens out over time. And by that I mean yes he can expect someone to take on the bulk of the cooking if you're at home but expecting a hot meal on the table at a certain time, or s favourite shirt washed and that kind of thing is unrealistic with young children.
You're presumably at home to look after young kids, not just because you dont fancy pulling your weight, and he should be pleased that you are helping him out by doing his share of his household chores, not having a go like You're a paid employee who has fallen short of meeting their expected targets.
Also even if your set up is more traditional where one person does home and one does work...there is a certain amount of being thankful for what the other person does...and this works both ways. If he wants it where you both have to live up to each others standards then youd be within your rights for having a go at him for not doing better in his last review or not reaching promotion quick enough.
If he is a surgeon my bet is he is used to barking out orders at people at work and have people running around after him and he isnt grasping that the same hospital hierarchy doesnt apply at home, at home you are meant to eb equal partners
Also if he was single he would have to organise his own bloody washing and food - having a job with long hours doesn't exempt you from any household tasks