You are correct, Voc. Rehab does not offer BAH; that is part of the GI Bill.
http://education.military.com/money-for-school/gi-bill/new-gi-bill-overview
Monthly Living Stipend
As an
eligible veteran or member of the National Guard or Selected Reserve you may receive a monthly housing allowance (living stipend) based on the ZIP code of the location of the school you are attending - not your home ZIP code. This stipend currently averages $1,200 a month, but can run as high as $2,700.
This stipend is based on the DoD's Basic Allowance for Housing (BAH) for an E-5 with dependents. This stipend does not require students to live on campus.
NOTE: Servicemembers currently on active duty and veterans (and eligible family members) taking courses on a half-time or less basis and/or taking 100% of their classes at a distance (online etc.) do not qualify for the monthly housing stipend.
Check out the Military.com GI Bill Calculator to get an estimate of how much you can get under the new Post-9/11 GI Bill.
Resources:
http://www.military.com/money-for-school/gi-bill/new-gi-bill-overview#hs
http://www.military.com/benefits/military-pay/basic-allowance-for-housing-rates