Are you allowed to use military BAH (basic allowance for housing) as line of credit to buy a house?

Well, if this is a 15-year or 30-year mortgage, do you plan on receiving that BAH check every month for the next 15 or 30 years? And is that actually earned income, or something that can just stop being sent to you suddenly? If I was a lender, I'd be looking into the far future, not just at the fact that you happen to be receiving this BAH check right now.