I think we have a pretty even split of roles - probably because he took 2 months of paternity leave when I went back to work full time, so we both have a very clear idea of what needs doing without one person managing the other. He can also use the school holidays to do a lot of stuff (teacher).
I do all meal planning, shopping and cooking (I find it relaxing). He does almost all tidying but I won't let him touch my home office which drives him mad as it's a tip.
I put in washing, we sort and put it away together while watching tv. He does pretty much all ironing.
We currently have childcare but soon I will be responsible for kids and school run Mon, Fri, Sat. He will be responsible Tues, Weds, Thurs. (This includes sorting out childcare cover if we need it.)
He does bath and bedtime every night unless he has to stay at work late (1-2 times a week).
He does bins and garden. I do all DIY, flat pack furniture, and car repairs.
He does insurances, utilities and presents/cards for family. I plan holidays and we organise savings and financial planning together.
He organises kids doctor and dentist appointments and haircuts. I organise school uniform and kids clothes and shoes.