Umm...well he considers "cleaning" more like tidying up and organizing but not actually CLEANING with products - but he does vacuum.
Cooking: He does the grilling in the summer - but winter its all me.
BUT he is really good with money as I am NOT so its an even trade!
Our rules is simple -
Kitchen: If I cook, he does the clean up and dishes. If he cooks, I do.
Cleaning: I take care of the inside of the house, he's in charge of outside.
It works for us.
Yes, DH helps with both. I do more cleaning and we take turns cooking.