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)

Simply put I was honored to serve and I don’t over analyze it. When I'm told "thank you for your service" I respond with "thank you. It was my honor"

So after I finished my osut I got stationed to JBLM, my husband was still in Fort Hood. I couldn't get BAH until he followed me to JBLM.

You should be both living in the barracks w/o dependents so No there is actually no reason to pay either one BAH. Both of You can apply for BAH W/O dependents by submitting a 4187 However it Must be approved by the Company Commander which unless you have other mitigating issue is rarely approved. The housing is available so why pay you all and let the furnished living area sit empty?

Just curious. Did you request an assignment together through both training and at your permanent station, when you enlisted? The reason I ask, is when I enlisted (a lifetime ago) they had what they called "the buddy program" where my buddy and I (from high school) were given a guarantee that we would be assigned together at Basic and also at our permanent base, after AIT (we had no guarantee for AIT; because we had different MOS's). I would think that, with today's enlistment numbers being so low, the Army would at least do this for married couples.

You are qualified for the Basic Allowance for accommodation (BAH) if you are a member serving on permanent active duty within the country but are not residing in any government-funded accommodation.