Oh, mama, I went through a lot of similar emotions towards baby/parenting/DH when I had my first (colicky, high touch needs, exhausting, wonderful) son. I can say, bear in mind that men don't know what to do with infants, and it's not that the don't love them, but my DH told me, "I can't think of the baby as a real person until he can communicate with me." Your DH may feel similarly, and he may not be able to read baby's cries as well as you can. Again, I quote DH, "It all just sounds like CRYING to me. It's loud, it's irritating, and I want to run away. I don't know what the problem is."
I can say, as somebody who tried unsuccessfully to work from home, he may feel that if he's working
, he ought not be coming out to hang out with you. Maybe you can have him take a "lunch hour" or some breaks to take care of baby while you take a shower, but it's tough to balance WAH with baby care. They are sort of mutually exclusive, in my experience, anyway.
Quick antidotes to exhausted and depressed are hard to come by. I can suggest getting yourself out of the house and finding some more social support, even a postpartum doula or teenage girl who comes over after she gets off school for a few hours to give you a break or help with washing dishes. Women were not meant to be the sole caregivers for infants 24/7. That's a fallacy of attachment parenting. Can you get out of the house - breastfeeding support group, babywearing meeting, playgroup meet-up at a park or mall, mama and me yoga classes, church social, anything to start meeting people and building your social support network?
If you are pumping, then I also suggest that you and DH take shifts for feeding baby at night - you sleep from 7 p.m. to 1 a.m. and he feeds bottles of breastmilk, then he sleeps from 1 a.m. to 7 a.m. and you nurse when babe is hungry. That way you both get 6 hours of unbroken sleep. You have to take care of yourself - sleep dep. and isolation and "this isn't how I thought it would be" are a recipe for wicked bad PPD. BTDT, and take care of it NOW, not in a year. Also, consider that your DH is probably very stressed too, though he may be losing himself in work to avoid looking at it. Maybe he is depressed and struggling too, I think this is a good thought to keep when you are getting mad at him.
Mama and Wife are both tough roles, and nobody really tells ya that upfront.
Also, if baby is crying a lot, the 5 Ss (Harvey Karp - shushing, swaddling, side/tomach holds, swinging, sucking), bouncing on a yoga ball, babywearing, and taking baby for some chiropractic treatments might all be helpful.
Your DH might find that he's good at soothing baby with deep humming or singing with baby held against his chest (they like the vibrations of the man's deeper voice, and they can hear his heart beating), and if he can find his competencies/strengths as a dad, that will also help him with feeling more connected to baby. But, really, you are the go-to for baby right now, and you will be chopped liver and Dad the all-star by the time baby is a 5 year old.