DH and I separate chores into your job/my job. This works for us. We have daily and weekly jobs.
One of my jobs is the washing, and one of his jobs is cleaning the kitchen. We share the day-to-day wiping down of surfaces, but the proper weekly clean is up to him.
He thinks that because I do the washing, cleaning the machine is my job. But I think that because the washing machine is in the kitchen, it's his job. Also I do the cleaning of the inside - run vinegar through it etc - so I think wiping down the door and the bit that sticks out from under the counter is in his domain.
Who is right? YOU DECIDE! Please note that our marriage does not revolve around domestic minutiae and the ongoing dispute is more of an eye-rolling joke than a symbol of irretrievable relationship breakdown.