I'm also sorry to hear that your OH is useless, and spiteful with it. So my suggestion is consider yourself a single parent, He's not going to help. You may be able to get him to agree to, say, doing dinners but don't bank on it,.
What I am suggesting is that you read "the contented little baby book" by Gina Ford or something similar. Get baby into a strict routine, and yes they do thrive on it unless they have tummy troubles or something, It breaks down the looking after baby 24/7 into chunks of time when you are interacting with baby, and chunks of time when they are at rest or asleep. This way you know when you can have your lunch in peace or a nap,
Baby is still very young and things will change back and forwards; what are your thoughts on co-sleeping, amazing how well that works. Or at least feeding lying down, i didn't know you could with my first, if only i'd known, it works a treat and once again you get a rest.
All the best, expecting help that isn't coming is more exhausting than getting on with it yourself. if you stop asking for help he'll either come forward or you will know he's not for you,