In the US, you can be fired for almost any reason or no reason at all.
In most states he can be fired (or quit) at any time, with, or without, a reason.
contact your local unemployment office and ask for information about your local labor board. it all depends on the contract(s) your husband signed when he was hired. you can file a grievance, but if you win you won't get your job back, but at least you can let new employers know that you were unjustly terminated. I had to do this several years ago, and I had my daughter do this as well when she was terminated at a job when she was a teenager. we both won our grievances.
My husband's boss terminated him from his job yesterday. The reason given was that he "found out" that my husband put in a job application at another company because it paid more money. It turns out that he didn't get hired but it doesn't seem that this is a good enough reason for firing someone. Does anyone know if this is legal or do any of you have any advice??