I have a Navy BAH question?

I am reading through my US Navy DEP START book and under moving your family it states if government housing is available you will not receive BAH. Does this mean I have to live on base where I am igned if its available and if I don't want to they are not going to pay me BAH. I can't live on base due to the fact I have 3 dogs(2 limit) which 2 are bully breeds(most don't allow bully breeds). Does anyone know how BAH works once you get your ignment? I don't have any kids but I am married.