Perhaps other people could tell me what their DHs do?
Here are splits for three couples in my family. We all seem reasonably happy with our lot except where the issues are caused by personal preferences differing - e.g. one partner wants a tidier house than the other. Who does which precise job seems less important than finding a balance that works for you.
I would say that I think it is vital that anyone can do the basics of cooking and laundry as you never know when you may need to take over due to illness. Both of my grandfathers had to look after themselves for 10+ years due to bereavement/illness. Jobs like DIY and cleaning can be outsourced but even then it's good to have an idea of what's involved.
Pre-child:
Me (30s, full-time work): all laundry, most of the washing-up, most cleaning, assisting with DIY, any mending/sewing, most of the tidying/decluttering.
DH (30s, full-time work): all cooking, all food ordering, DIY, assisting with cleaning and decluttering (e.g. hoovering when I was heavily pregnant).
Whoever sees it needs doing: putting out bins/recycling.
Things done together: financial planning, ordering birthday presents.
Things that only get done when really needed: ironing, gardening.
On maternity leave we are continuing to do the above, but with a bit more flexibility depending on who is more tired - e.g. DH will put a load of laundry on if I haven't managed, and I'll make sure he gets a lie in when he has a lot of work deadlines. When I go back to work (full-time with DD at nursery) we will probably hire a cleaner so that we can both spend more time with DD when not at work, and we'll discuss rebalancing the remaining housework as well.
My parents:
DM (60s, SAHM, then lots of voluntary work): all cooking, washing up and laundry, some cleaning, most ironing.
DF (60s, worked FT, now retired, also doing lots of voluntary work): cooking, laundry and ironing when DM is unable (mostly through back problems), all hoovering, most of the cleaning. He also does the gardening, bins, car maintenance, financial planning and DIY - and has always done these while working.
Things done together: household organisation and buying presents.
They are still rebalancing - DF prefers a tidier house than DM and so is doing more to make this happen than he did when at work.
My parents-in-law:
DMiL (60s, worked FT, now retired, lots of interests): cooking, financial planning and cleaning, her own ironing, some gardening, bread making, all the household organisational planning, ordering presents.
DFiL (60s, works FT, due to retire soon): some cooking/baking, his own ironing, a lot of gardening, DIY, most of the decluttering.
Whoever sees it needs doing: putting out bins, recycling.
I think they share loading and unloading the dishwasher but I only see what happens when we stay - at which point we all help and the only rule is that the person who cooked gets to opt out of washing-up/loading the dishwasher! They had a cleaner when DMiL worked full-time. It'll be interesting to see what happens when DFiL retires - I hope he does more cooking as he is good at it!