Stop doing whatever it is that you do all day, especially whatever you do for your H.
No cooking for him. Make yourself beans on toast or whatever. Don't do his laundry.
Forget about hoovering, tidying, cleaning the bathroom.
Try to get out for a little walk with the baby though.
Get yourself decent earplugs and sleep on the couch. He can do Friday, Saturday and Sunday nights, for starters.
Leave a bottle or two of formula or expressed milk for H. Leave the baby and H in the bedroom. Tell him to talk to the hand when he refuses. Show him the hand, and the fingers if necessary, and lie down on the couch.
Babies sometimes accept the bottle from someone other than their mothers, and babies will sometimes accept formula from a dad before breastmilk too. So he needs to be left for an extended time with the baby, in order to learn how to deal with being a parent.
Please consider heading out by yourself -- to a library or to the cinema or to have a massage or just to sit and sip some coffee and look around the shops, and leaving H and baby to get to know each other for at least three hours each weekend day. Bring your pump if you have one.
Is there always poo in the nightime nappy? If just pee, then don't bother changing the baby. A quick sniff will tell all, no need to undress the baby and peel off the nappy.
Get a tandem cot/bedside crib/bssinet? They clip to the bedframe so you can cosleep without being all crowded together and you don't have to get up to put the baby down. Put it on DH's side of the bed. www.nctshop.co.uk/images/4383.jpg Try not to throw something at that picture. I hate images of clearly well rested women with their small babies.
Talk to your GP or HV about the thoughts you are having.
Tell her/him especially that your H is a useless lump who is too special to act like a grown up husband and father and whose precious work is more important to him than his exhausted wife. Do not mince words. Ask her to read him the riot act.
And Shame -- tell your friends what a knob your husband is. Maybe one of them has a husband who could take your H aside and tell him he is being an arse.
Tell your family too, even though they are so far away. Someone needs to kick your H's ass.