The Basic Allowance for Housing, or BAH, is a stipend paid to military service members who do not live in government housing. It's intended to help them afford a place to live. As far as the Internal Revenue Service is concerned, military BAH is not included in gross income, and is not taxable. But there are other contexts in which the allowance may be considered income.
Why It's Not Taxable Income
When a service member lives in government housing on a military base, the value of that housing is not treated as gross income to the service member. This differs from the civilian world, where employer-provided housing usually counts as a taxable fringe benefit. The military service member doesn't have to report the value of base housing as income on his tax return, and he doesn't have to pay taxes on it. Excluding the BAH from income simply extends this treatment to service members who live off-base. In both cases, the service member's base pay is subject to income tax, but the housing he receives is not -- regardless of whether that housing comes in the form of an actual place to live, or cash to pay for a place to live.
Other Contexts
Beyond tax purposes, a service member's BAH might be considered income, depending on the context. For example, federal courts have ruled that states can include the housing allowance in income when calculating child support obligations. The BAH is included when calculating income to determine eligibility for food stamps, and states are allowed -- but not required -- to use it in determining eligibility for the WIC supplemental nutrition program. When applying for any program, benefit or service whose eligibility hinges on income, it's best for the service member to ask directly whether to include BAH.