DH is DCs primary carer - he does work, but a limited number of hours to suit school runs etc. We used to have a cleaner for the heavy work. Now kids are are school, he does it. But to give you context as the working parent what I do:
Most cooking and big shopping (although this is a small bone of contention as DH just doesn't cook and I mostly accept that and he's can and will throw together basic stuff when needed but...He does handle 90% of the day to day shopping now though eg buying fresh bread, milk, fruit etc).
The odd bit of laundry, particularly on weekends but usually no more than one load a week.
Most weekends I will do one thing of cleaning - eg the kitchen, bathroom etc, usually while listening to a pod cast or while otherwise generally pottering.
School uniform and clothes shopping and maintenance (eg fixing/alterations etc)
Plus of course my fair share of bed and bath time, daily tidying/cleaning up after dinner etc.
I also do most of the "thinking" work.
Working parents with SAH partners who do nothing make my blood boil.
I point blank refuse to do things like washing in the evenings - I think there's plenty of time during the day to put a load on and I'm not interested in hanging up washing at 9pm. Ditto, I'm not going to run the hoover around unless there's been spillage. But that doesn't mean I abdicate all domestic responsibilities.