Ah, sounds like you have daddy issues as well as baby ones
If he wants housework done so badly, he'd better start doing it, hey? Has he spent much time alone with your baby, actually trying to cope with it? If my DH comes home to a clean house he congratulates me in wonder! He was a SAHD for a while with DS so understands very well how little you can get done with a demanding baby.
Is there a father role model you know amongst family or friends who could talk to him perhaps?