DH and I both work full time - I do think that helps; if one person is out of the house working and the other person isn't, a sense of unfairness creeps in.
DH does the laundry, cleans bathrooms, hoovers the difficult bits like the stairs (we live in a 3 storey house and I hate doing stairs) and does the dusting/wiping down of surfaces as he goes, does at least 50% of kitchen cleaning and well over 50% of clearing table/stacking dishwasher. Empties all bins and does the recycling, mows the lawn. Sorts out packups (I make the sandwiches). Does all the bill-paying/insurance type stuff.
BUT he didn't always do this much, and when I was off on mat leave he gradually did less and less. Not at first, as DS was prem and spent a lot of time in hospital, but after the first couple of months I seemed to be doing more and more. I didn't mind then as I was at home all day, but when I went back to work he didn't suddenly leap into action again.
We sat down and each wrote a list of all the household tasks we could think of, and then who was responsible for doing them. I think it shocked him a bit and he was happy to take on some of the areas. It's the key thing, that responsibility - otherwise you end up 'asking' them to do tasks that are actually household responsibilities and they think they are doing you a favour if they do it once! Could that work for you?