Not as much as me, obviously, but not nothing either.
He does his own washing and ironing - he has his own washing basket and sorts it out himself. Every second Sunday he will iron 10 shirts which lasts him for the next 2 working weeks.
On the weekend I tend to leave the packing and stacking of the dishwasher to him. During the week I tend to at least unpack it, and often stack it too.
On the weekend he tends to catch up on the recycling by emptying the recycling bucket, putting it into the relevant bags out the front etc.
He takes the children to swimming lessons on a Saturday, which for me is a major faff which I hate, and takes my son to Rugby on a Sunday, which is at least an hour of standing round on a cold field, which is once again invaluable!
He'll also put them through the shower on a weeknight if I haven't already, and do their reading with them.
He doesn't do all that much else - I do all shopping and cooking, I have a cleaner once a week but do all the other incidental cleaning stuff, washing for me and the children (he'll sometimes help by getting the children to sort and put away their stuff if the clean washing has built up during the week), hoovering, basically I do "all the rest". We have a man come and do the lawns.
So he really doesn't have to do very much at all - but he's not here all that much during the week, and the things he does do when he is here are things I really hate doing, so I never feel like I'm being used or put upon. The only thing that makes me feel martyrish and irritated is when I've cleaned something and the children trash it within seconds with crumbs or whatever, in which case they are directed to make it right or face my wrath.
For context, mine are 6 and 8 and at school during the week, and I don't work at all, so I have just under 6 hours a day to "myself" to get done what I need to get done, and that's enough time to do some DIY type things as well if I am that way inclined.
When they were toddlers and babies and there was somehow more to do, more often, he did more when he was here - things tail off a bit. Still feels like groundhog day sometimes, but at least there is no Weetabix drying on the wall like concrete...