What re my rights regrding a rescinded job offer?

Your husband might not have recourse: if the offer was for immediate employment but he did not simply accept, but rather stated that he needed to give notice, what your husband did was to reject the job offer and make a counteroffer (i.e. I'll work for you if you let me give notice). Unless the potential new employer clearly accepted your husband's counteroffer, they would not be bound by it; and since your husband rejected their initial order, he could not enforce it against him.

On the other hand, if the new employer did accept his counteroffer of working for them after he gave notice to his current employer, he may be able to enforce that agreement against them as a contract. However, even in that case, if something came up during the call with the old emplohyer that cast your husband's work or qualifications in a bad light and which he had not previously disclosed to the potential employer, that new information may be enough to let them rescind their offer without penalty.

Therefore, the odds are that your husband does not have recourse, but it is still possible he does, if the new employer accepted his counteroffer of starting to work for them after he provided notice and if nothing came up during the employer phone call which would provide valid grounds too rescind that agreement. If your husband thinks this may be the case, he should consult with an employment law attorney about the situation in detail to explore his possible recourse.