DH and I also share the jobs, although, like in your situation, I usually have to ask for certain things to be done (except the kitchen, he seems to realise when that needs doing).

I do the whole list thing. If he is home for the day I often leave a note mentioning a couple of jobs to be done (even as simple as washing - DH never notices of the basket is overflowing). Some weekends if there are lots of things to do I'll make a list, leave it on the bench and we will both pick things from it until it's done.