Dad here, I've been in the situation your husband is in.
Speaking from my experience, there was a lack of appreciation on both sides. I didn't appreciate how hard it was being a stay at home parent, and my wife didn't appreciate how hard it was having a career. Both sides can grow resentful of the other side. My wife for example, craved the adult interactions I had at work, and I was resentful as I viewed "staying at home" to be easy. There's also the whole money aspect, being the only person contributing financially can be hard to accept.
Getting a job is not the solution. It just adds more things for you to do, for minimal financial gain, and less time to do chores, family time and time as a couple. Who does the house work? Who picks up kid from childcare? Who does the shopping? etc, etc.
For my family, since January we have turned the tables around. I am the stay at home parent and my wife goes to work. I can 100% say that it has been a real eye opener for both of us. We have a renewed appreciation for what each other does.
I would encourage an open conversation about how you both feel, taking emotions out of the situation. Trial some creative ways that you can live in each others situation. Perhaps even discuss how you can contribute in other ways that don't involve financial contribution.