In my family I am the CEO when it comes to the kids ie I organise the Childcare, immunisation, pack snacks for when we are out, buy all the kids things eg toys and clothes etc. I also see this a lot with my friends where it's the mums who pack the kids things, organise outing for the family, buy all the kid related stuff etc.
In terms of housework dh does his share. Overall I think we have a good set up with dh assuming responsibility for finances, car, yard work, house maintenance. It's a team effort but i do see it as each having primary responsibility for different aspects required to raise a family.