I have this as an ongoing problem, but through a lot of talking, its got better.
We both work FT, so we split the lie-in at the weekend: either of us can lie in until 12 if we want to.
Evening childcare is split if we are both at home in time, although I do have to do some chivvying along.
Evening cleanup is shared (put away + sweep + dishes etc), again with some chivvying
and then... I do all the rest! (er, washing, tidying, putting away, household admin). We outsource ironing and have a cleaner 1 x a week.
He does bins when he remembers each week and does the garden in the summer.
Still rather S**t in my opinion and causes lots of arguments. It would be more balanced if I did all laundry (happy to do that) and he did the general tidying.
I agree that if he works late nights, he might need more leeway in when he gets up. The being p**sed off at having to go to the park with DCs is just wrong, in that he sees it as boring, rather than good & essential family time, and fun for the kids.
I also had an issue with DH in this area, in that he'd taken them out about 3 x in 3 years.
How old is he, out of interest?