Unemployment rules differ from state to state. Speak with your local Unemployment Agency and read your local laws. In some state's it's an issue and in some other state's it's not.

Is your husband capable of physically working at a non-construction job? If not, have it documented. Has he been to a Voc Rehab Agency? If they're unable to help him, that is one way to get additional documentation, but they might be able to retrain him in spite of his injuries...