Do the overtime or be suspended?

What they are doing is not legal. Forcing someone to work with no pay is called SLAVERY. I would continue to work, but also get a lawyer and bring a lawsuit against the company. If you he can clock some hours in which he was coerced into working under threat of termination with no pay, than that counts as forced labor. You may be able to sue for a lot of money. Like I said, log the hours, keep a record al all unpaid work, and quietly talk to a lawyer. This seems to be a clear violation of your husbands civil rights.