Next time he says you've to ask him for help, ask why since he's so horrible when you do!
As for housework, he's being an absolute dick. It's his house, his kid and he does fuck all. Unless he's living in the 1950s, coming home to a spotless house and a wife who does absolutely bloody everything despite being exhausted is completely ridiculous.
If he wants a spotless house then I suggest he gets his marigolds on and cleans it!
He should also be doing night feeds, especially if you ask him!
DP is deaf in one ear, and didn't hear our babies in the night. However, if I was wiped out and woke him to do the feeds, he did, every time.
Not because he's some kind of superhero, but because he's not an arse.
I'm sorry your husband is being so horrible, I hope he gets a grip soon.