From Rod Powers,
Your Guide to US Military.
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Below are the rates of tax-free housing allowance (Basic Allowance for Housing, or BAH) that are provided to military members (with and without dependents) who are authorized to reside off base at government expense.

Enlisted (with dependents)

Enlisted (without dependents)

Warrant Officers (with dependents)

Warrant Officers (without dependents)

Commissioned Officers (with dependents)

Commissioned Officers (without dependents)

Note: BAH amounts are determined by location, rank, and whether or not the member has dependents. Between ranks, amounts differ because the higher the rank, the better the housing a member is authorized. Here are the charts that show what type of dwellings are used to determine BAH amounts for each rank.

There are specific rules which determine whether the military member is paid the housing rate for the location of his/her assignment, or the location of his/her dependents. This chart displays those basic rules.