This situation sucks but it is by no means unusual. I know plenty of people in this situation. The good news is that it will probably change real soon. Qatar has applied for membership of the WTO and a condition of entry is free movement of labor. Relying on an NOC is clearly a restriction of labor movement so it will have to change. I do not know the timing on this but I understand it will be soon within the next few months.

In the meantime, your husband can get another job on a monthly contract until the situation changes. He and the rest of the family will not be "officially" resident in Qatar but you will be legal provided you all do the visa runs. Its not ideal I know, but it should work until the law changes and he can change sponsors.