I do all the cooking and food preparation, including menu planning and shopping. He gets his own breakfast, of course, makes himself cups of tea, a sandwich for himself on the weekend, etc, but "dinners" are done by me and all the food is there in the cupboard without him having to do anything.
I do the lions share of the day to day cleaning - but not all of it. His "job" is unpacking and stacking the dishwasher, and on the weekend, he does a series of really thankless stuff in the utility room including the cat litter tray, nappy bin, bagging up of the recycling, putting out of the bins for the bin men, etc.
I will put a load of washing of "his" on for him (we have separate washing baskets) and load it into the tumble dryer, generally I'd ask him to sort/process this himself though, on the weekend (I wouldn't mind if it sat in the basket till then). He will also initiate the putting on of washing of his own if his basket is getting full. I do all mine and the childrens.
He does hedge trimming. We outsource lawns. I dont really do "outdoor" stuff. I get the car washed by the illegal immigrants helpful gentleman at the hand car wash. We fill our own car with petrol/diesel, we each have one.
Generally he doesn't do any cleaning outside of the kitchen - he "mucking out" the highchair (!), and general kitchen cleaning. There are certain things he never does because I just do, like floor washing and bathroom cleaning (though he leaves it in the state he finds it and puts the seat down) - I just tend to do them before he would think to. If he's feeling like mucking in for some reason, say we've got people coming over or something, he tends to gravitate towards hoovering. He'll happily get involved in glass cleaning etc if asked, doesn't tend to be proactive but will happily muck in with anything and is great at getting the kids motivated to "help".
More recently I've been asking him take on encouraging the children to clean the play room and help them with that (they are very young)
Flat pack is him.
He doesn't have to worry about any child stuff - I am a SAHM. If they need the doctor, I do it, I buy all their clothes, everything is organised and provided and sorted for them with nothing required of him though I communicate decisions or choices to him.
Generally, he'll come home from work at 7:30pm to a hot home cooked dinner, kids fed watered bathed and pj'ed, and a relatively tidy house.
We never argue about housework, roles, etc. He always treats me with respect and me him. Actually we never argue at all. Last time we argued was 2 weeks after my son was born and he bought the wrong bottles and I went berko a bit hormonal. Son is 3! So I guess it works!