Your situation sounds much like mine when we had our first 2+ years ago. My DH is a medical resident, and we moved to a new city with a 5-week-old newborn. He had done ALL the work for the move because we had a baby--he set up all the utilities, did the vast majority of the packing, unpacking, and setting up. Then, we got where we were going, and he started his residency--really stressful, new situation, new material, new people to impress, little sleep, etc...
I was home (had quit work just before baby was born), hadn't met people, had a fussy baby, couldn't sit baby down to pee let alone clean, and baby would only sleep on my lap after nursing--could not be moved. No friends. Dogs to take out to pee on leashes, and they barked and woke Nora up.
It was hard. Stressful. We had never had ANY stress in our relationship, and I kept turning the thought of, "what do I need him for? This would be easier at my mom's" over and over in my head. DH had a hard time bonding to the baby, and that was reall stressful to him. I think he felt very much like a failure since he didn't respond to her the way we both expected him to. It was a really hard time.
One difference was that my DH did realize that I was doing a lot of hard work and was suportive. But he would roll his eyes when I'd ask him to hold her so I could shower and things like that. (that still makes me fume thinking about it now!)
Things got a lot better for us. DH grew to like and love the baby after 4 or 5 months (shen she stopped crying all the time and we moved her out of our bed--he was supportive of having her there, but I felt like it wasn't working right for us), and he is now a wonderful father to her. He has had a much easier time adjusting to our2nd baby.
Things that helped me were to talk to him about how I felt when he was well-rested and baby was not crying. I met some people--luckily there is a great group of women all here with kids becasue of their husband/partner's residencies. That was great. I met one woman and made a good friend of her in the grocery store. I met another online. A few at the park. ANYWHERE I COULD!!
This is a hard transition for you both. It will get better. the baby gets easier. You will get things done again--but it may be a long time before you feel like you are being as productive as you feel you should be. For me it was at about 15 months. Seriously. I was doing much more than I was at 6 weeks long before that, but it has yet to be even close to that image of the 1950's mom. Maybe it just took me that long to drop the "shoulds".
Stacy-- Wife to my DH, mom to three: noodle girl:, Lego boy , little guy :