It sounds very hard.
As a person with self-esteem issues, I can relate to your husband. When I get a new job, I feel like I have been sentenced to six months of When-are they-going-to-fire-me land. I don't have any idea how to decrease the fear/anxiety that I feel when I get a new job. I suspect your husband may have a high level of anxiety in new jobs too. He also sounds like he copes sometimes by denial. I have an amazing capacity for denial too. Patience is deffinately a must in your situation. However, it is something that I doubt I could have.
Is there any kind of side job that you can do to make money from home? Would you consider babysitting some other people's kids with your kid? That is a way to make some extra money and still be there for your kid. Is there any kind of budget cuts that you can make? Since the reduction in pay is 40%, I suspect that this going to be painful for all of you. I make 8 dollars and something an hour. So, I know how unpleasant tight/tiny weenie budgets are.
Well, I hope you can live through this and reach better times.