I'm a stay home mother but spend between 10-15 hours out of the house a week for volunteer commitments.
I have 4 kids aged 6, 4, 3 and 2.
6 year old goes to school, 4 and 3yos are in preschool Tues/Wed/Thurs. 2yo is with me all the time. Tues and Thurs I am out for volunteering so Wed is my only day home with just one kid.
I try to do most of the big housework on that day. I also try to keep the kitchen and living areas tidied and neat. Hubby works shift work so if he is on nights or afternoons, I don't really get any help at all. If he is on day shift or day off, he might volunteer to cook dinner (he doesn't mind cooking). If I ask him to run a bath or dress the kids he might do it. But I am generally in charge of that and bedtime. I do all the washing etc. he recently bought me a dishwasher as doing the dishes with my carpel tunnel was becoming unbearable and while he "took on" that job, he just fell behind and I ended up doing it all the time.
He does some outside work if he feels up to it on his days off.

Sorry, it's getting a bit scattered. Basically speaking it's tidying, vacuuming, washing, dishes, cleaning bathrooms, etc (general housework) I do myself and try to have it done while he is at work.
Dinner is probably more me (due to his shifts) but 50/50 on his days off.
Bath and bed routine is mainly me unless I ask for help.
Outside tidying is done by kids. We live in drought area so mowing is rare.
We see specialists for my 4yo (autism) every fortnight. I go to OT while hubby has the other 3 children and hubby goes to speech while I take the others. Grocery shopping is done on the same day (we have to travel to do these things) so it is done together. I generally unpack and put away the groceries. He does the meat.

He does help out more than some men do but I think he also gets it a lot easier then some others.
Apart from when the kids at school, I don't take "me time" away from the house. That is, it is exceptionally rare for me to leave the kids with hubby while I go out. Including running to the servo for milk. I do all those things with kids in tow generally. I have been out with friends without the kids once in 18 months for an hour. He also had them on his own twice a few weeks ago while I was out doing the volunteering but they were sick home from school. I do usually take them with me if the volunteer stuff falls out of school hours, even if hubby is home. So he doesn't really have that responsibility.