My DH works a part-time schedule, opposite of mine work schedule, and stays home during the day.
When I get home, I take my son and pretty watch him the rest of the day, except for if I'm making dinner that night. I often take him to the park as soon as I get home, so DH has some quiet time in the house by himself (he's an introvert & really needs it). I also pretty take care of our son on the weekend with only some help from DH, as he sometimes works, and also just needs to unwind.
One night per week, DH goes out with friends. I encourage him to do so, for his sanity. But he also really appreciates having the house to himself for a couple hours while I take the LO out of the house.
The newborn stage, up till about 6 months, was the hardest for DH, but it got easier (newborn was hardest, and it got easiest over time).
For during the day, when you can't give him a break, here are some things to try, so he doesn't feel so trapped in the house:
If the baby is small, you can use a carrier or stroller and go for walks, even just around the block to get out of the house. If the baby is toddling, take him/her to the park for playing is a great idea. My DH & son go every day if the weather is good. They also go to story time at the library -- check with your library to find out if they offer it, or if a nearby library does.
Our metroparks system offers programs for toddlers & preschoolers as well as older kids/teens/adults, and they will occasionally go to that.
You can also google your area and "stay at home dads" -- there is usually at least 1 SAHD group in most metro areas. Your DH might feel more comfortable doing play dates/activities with other dads than with moms. My DH is not much of a "joiner" so he has not really gotten involved with an parents groups.