This sounds just like my first H. We met through work, both working in the same industry in which at the time it was fairly easy to move around and find new jobs.
We both started work at the same place in the same week, started going out, fell in love and got married in the space of a year. Both still working together. Not long after the wedding he said we should both leave the jobs and look for other work. Without actually having other jobs to go to before quitting. Being v young, foolish and in love I agreed.
I secured work not long after, he embarked on a pattern of finding a job, stating it was the best job in the world, so much better than the last one. Then some minor niggles would creep in, it wasn't such a good place to work. Then it was awful, they didn't appreciate his talents, he wasn't happy, would start missing work altogether, they would then part "through mutual agreement" and he would be unemployed for a while.
In the meantime stupid loved up me was still working at the same job wondering why his talents were so unappreciated and keeping the home running on my wages alone.
We didn't have kids. Thank God.
I gradually recognised the pattern that was playing out in front of me, each time the cycle repeated it was a bit quicker and by the end was taking three to six months each time.
I was still in the same job after eight years and didn't want to move around in case I jeopardised a steady income. Finally one of my work friends took me to one side and said that she felt he would never change, she knew of other relationships where one partner would behave like this and the other was always left to pick up the pieces and she felt I was worth more than that.
It took me another year to separate from him. And I was a risk averse wreck at the end of it. And yes he felt I was unsupportive and overreacting. However although after we split I missed him and we'd had good times together I found I didn't miss the constant "on edge" feeling wondering when he would start finding his latest job unsuitable.
This is one very biased viewpoint but it really really isn't worth spending your life feeling like that. You come to resent your partner for not contributing equally and equally resenting them not recognising when they are failing to do so. Resentment in a relationship is a killer.
Sorry to hijack with my own story, I don't often re-visit those times in my head but your circumstances struck a chord. Good luck whatever happens.