For us it's a direct split:
He earns and pays bills. He builds a career (not something I'm interested in) though I do have pursuits but won't clog this thread with them.
I collect all the dishes, laundry, wash, fold, I do all the meals, three a day, I home educate our child. I empty the litter tray - I do all the domestic tasks OP. All of them.
He does not lift a finger in this house because he pays the bills. I do not pay any bills because I keep the house.
It works for us as it works for many. I like it.
Having said that I have the benefit of having lived a whole life before I had kids. I was 34 when I got pregnant so I am more than ready for this domestic bliss. I'm tired. I'm a homebody. I love my routine. I have coffee in bed and tend to my day's activities.
In the evenings I'm prone to a glass or five of wine to be fair. I work for pin money in my freelance work, which I enjoy.
I'm a teacher, a parent, a homemaker, a wife.
He's a career man, father, and husband.
See I don't want mine to bath the kids or do much really as he will just get in my way. I will do all that and it will take me less effort to collect his dishes than for him to bring them down and leave them in the wrong place, basically (this is an illustrative example)
He's a great dad too.