We have three kids and I work days and my husband works evenings. We were blessed that our kids are pretty laid-back, and our youngest is a super sleeper and very relaxed baby. If he is prepared for the work he will have on his time home and willing to accept that you have to have much lower housekeeping standards, then it could work.
I get frustrated that my house is a mess, but I try to focus on health and safety hazards and not worry as much that my living room could never be featured in a magazine (unless it was for a makeover!). I'm actually going through wanting a fourth baby, not desperately, but I'll take as many as he's willing to try for. We would prefer NOT to have another until our youngest is closer to 2 (he's 7 months) and we have a house or larger apartment (we're in a 2 bedroom right now, but a great rental price/location/landlord, so not moving until we get something MUCH better).
You can totally care for 3 kids, but you will be fried a lot and just need to learn when and how to relax in order to cope. I was much crankier with my third pregnancy because my oldest stopped napping (he's almost 5 now) and I didn't get an after work nap. When my husband is home he encourages me to take an afternoon nap or an after work nap (he's off Fridays and Saturdays). You both have to want one more, but again, it is completely doable. I don't for a second regret our third. :)