I think the split depends on whether or not the two people involved are happy.
What works for one family doesn't necessarily work for another.
I have been a SAHM for 14 years. Some of it has been incredibly hard (poorly baby) some of it incredibly easy (like now.) I also have a medical condition that means I have chronic fatigue. Most of it is managed but if not then Dh, or either son, 16 & 13, will take over.
I have always aimed to do all the housework in school hours, and cooked all weekday meals. Dh loves cooking so he tends to cook on the weekend. He also loves spending time with the children and used to come home, take the baby off me, make me a cup of tea and leave me alone for 30 minutes.
The way I see it, when the working parent comes home then it is an all hands on deck situation.
Even now, with a 16 and 13 year old, after dinner everyone pitches in clearing the table, packing the dishwasher, hand washing anything that doesn't go in the dishwasher, wiping down the table and all the kitchen. We are all in the kitchen together, even if only 1 person is still working in it. We are a team. We talk, sing, have a laugh. As they say many hands make light work.