YY people moaning about their husbands not helping but also enabling them annoys me too.
I know you can't always tell before you have DC/you don't think about it in quite the same way though. I think I'm lucky in some respects that I lived with a right arsehole the first time so after that I wasn't going to put up with someone who didn't pull their weight or expected me to fill some weird "woman" role. And already had DC before I even got together with DH let alone married him, so I knew what I was looking for.
Anyway
DH tends to clean the kitchen/do dishwasher every day. I do it occasionally when I remember/think about it.
I tend to do the clothes washing, all of it unless I'm ill/really behind, then DH might put a load or a few through. This comes from an ancient agreement when we didn't have a dishwasher and the washing machine was in the cellar. I swapped laundry for dishes, because I despise washing up.
He will run around and stick the robot hoover on. I rarely hoover, but I use the normal one when I do because I CBA to wait for the robot one to finish and go and put it back on charge (we have a cheap one which can only find the charging station from one room)
Sometimes I clean bathrooms during the week.
On Sundays we all clean the house together - DH tends to do living room/kitchen/hall, I do bathrooms/bedroom, DS1 does his room, might do a bit of living room/bathroom if he is doing extra for some reason.
When we do the weekly shop we take down rubbish bags. I write the shopping list/do the shop online for pick up, go into the shop and pay. DH drives (I can't), looks after DS2 in the car, packs it all into the car and puts it away when we get home.
Cooking is probably 50/50 now - it used to be skewed towards me but DH wanted to learn how to cook.
DH does the heavy lifting of reminding DS1 to do his jobs/homework/teeth etc, I get up with him in the morning and make his lunch for school and tend to have emotional chats etc with him.
I buy DC clothes because I like to. Though SIL often sends clothes parcels, and DH encourages this because it saves money.
I feed baby except for one bottle DH does. We do nappies about 50/50 as he's on paternity leave still. I do bedtimes, but if he won't sleep DH takes him. We give each other free rein on naps etc.
I do most paperwork because supposedly I'm better at German
I still use google most of the time.
I seem to do all of the playdate/party/etc organising.
But I work PT and DH works FT.