Do both service members in a dual-military marriage get BAH?

A bit off the topic, but can you turn off your CapsLock key when posting? It's like shouting. ;-)

Is he in government quarters? Remember that you get BAH ONLY if you aren't living in government provided quarters. It would be rare in the Army that a Single PFC would be given BAH, which is how the Army will look at your husband since you aren't stationed at the same base.

It depends on whether or not you were married before or after orders, whether and when you were enrolled in MACP, and whether or not you both put in a preference for joint domicile (for family separation). If you were stationed together, and both living off post, you would both receive BAH at the W/O dependents rate.
Since you are not stationed together, the SM(s) that is in Barracks won't receive BAH since they are being housed in unaccompanied quarters.
If one or both of you are in the barracks, you could request an ETP from the CO authorizing off post housing and submit a 4187 (?) to finance authorizing BAH (Once again, signed off on by the CO. Chances of that happening in regards to a Geo bachelor PFC with no dependent are pretty low though).

All details regarding BAH and separation allowances/pay can be found in the Joint Travel Regulation. It can be very confusing, so I would suggest getting your first line to help you read through it.

(For reference, I am Dual MIL on an unaccompanied tour in Korea. When I PCS'd I "lost" my BAH since I was a geo bachelor and the dependent was under my husband. I got it re-instated by moving our son under me as the sponsor. We still "lose" money, as my husband is higher ranking and has more TIS, but it about equals out with Family Separation, Hazardous Duty Pay and COLA. Unfortunately for your situation a MIL spouse can not be considered a dependent)