My husband and I have done a variety of things over the years; I've been the bread winner, he's been the breadwinner, we've both worked part time. Right now I work four days a week and he works two, and we share the child rearing and domestic stuff between us.
The big challenge for him, I think, is finding ways to feel like he's doing something "worthwhile." (Not that I don't think domestic and child care stuff is worthwhile, but our society has devalued it for so long that it's easy to feel lost and diminished in it - something I struggle with too). So he does better when he has some work, even if that's a bit of consulting from home, than when he has no paid work at all.
He also does better when he has time and space to pursue his own interests and hobbies. Since our daughter was born he has written a novel, and even though there have been times I've resented the time that's taken, it's been important for me to see that as important and give him the support to do it.
The other thing that's been an adjustment has been the money thing; not that either of us feel diminished when the other earns more, but it's easier to feel financially vulnerable when you're not the one bringing in much of the money. So we had to do a fair bit of careful work on how we budget and communicate about money, to help manage that anxiety.
Some things are easier if you're prepared to pay to reduce stress levels. I'm prepared to pay for a cleaner to come through every so often, so that I don't get upset that he doesn't keep the home to my standard. And he needs to see why a clean home is important to me and accept the expense, since he isn't keen to do the work himself. That wouldn't be an answer for everyone but it helps our marriage.
I'm fortunate that he's always accepted my vocation to ministry and supported it, and therefore the flip side that as my husband, he has to do some of the stuff that makes that work. I don't think many husbands would have that level of humility and love.