When I was pregnant last year and on bedrest and physical restrictions (and then just LARGE and immobile), my husband did all the laundry. All the whites got kinda grey, but we lived. It was really exciting to be able to do the laundry again after the baby was born.
Nowadays, I do 95% of the actual operation of the washer and dryer, although the big kids are being trained to move their dirty clothes from their rooms to the laundry chute or laundry room. I sort the loads, run the washer and dryer, sort the clothes into three different baskets (Big Kid, Medium Kid, me-husband-baby) and then periodically put away the laundry from the basket for me, my husband and the baby. The big kids are theoretically supposed to put away the clean clothes in their baskets. Whenever they have free time and I remember, I tell them to each put away 20 items. I confess that our clean clothes spend a lot of time in those baskets. I also recently requested that my husband put a hook up in the laundry room, so that I can hang up his wrinkle-free dress shirts as they come out of the dryer and keep them wrinkle free–that is working very well. The most urgent laundry issue is that the big kids have school uniforms, PE and sports and need particular items washed up for particular days–the rest of us just need something to wear.
There are five different people wearing clothes in our household (plus various towels, rags, tablecloths, etc.), so it would be ridiculous to ask my husband to wash his clothes separately. I need to run two loads just about every day or disaster looms.
My husband does the dishes at night just about every night.