If he were to stop working for this guy and file for unemployment, they would first pull in all wages for covered employers in the last 18 months, roughly. This would, since hasn't been working very long for this guy, and I won't bet he's paying in his legitimate unemployment taxes on his employees anyhow, not include any wages made from this last employer (or owed to him by the employer) if there is enough wages there to set up a claim, then they'd look into the reason for his quitting the job and get a decision on this. It sounds like he does have an excellent job related reason to quit this job, so approval would likely be pretty easy.
You make it sound like the two options, reporting him to wage and hour and filing for unemployment insurance are exclusive, either or things to do. No, they're both things you'd need to do, if and when your husband does the really smart thing and stops working without being paid.
The bad news is that after you file for unemployment insurance, it will take at least six weeks for a complicated claim like this (where he voluntarily quit the job due to not being paid) to be resolved and for him to start receiving money. Then if the other old employer had some temporary or part time work for him, he could both work the part time job and draw a little bit of unemployment in some circumstances. But he needs to go on and file it, as it does take a while to get approved and get going.
As for reporting this dodger to the Wage and Hour people, it will take a long time to get repaid in most cases. Certainly not something you can expect to cure the situation in a timely manner. The longer your husband works without pay, the more he's going to be waiting for and trying to get back.
We are assuming that your husband is a regular salaries employee, that he did not offer to work for this guy as a contractor with a 1099 or anything like that. If he did, then small claims court is about his only alternative for getting the money back. Though all these entities, both the unemployment system AND wage and hour need to know about what this employer is doing.