Maybe you need to complain to your husband? Not in a mean way but next time he goes through his soliloquy, say "I know, it's horrible for you but I have to do this every night and don't get to play Nintendo".
Another perspective, if you're a SAHM, your husband makes it possible for you to focus on the tiny human by working so you can stay home. So even though he might not be perfect, at least he's there. Plenty of single moms have even less help.
Finally... would it be possible to go to bed at the same time as the tiny human, so that you get 7 hours of sleep?