UPDATED POSTED 16 Feb 2015
Maybe! The regulation I would refer to is AR 600-20. This is a matter of health, welfare, morale, discipline, and well being. However there are very specific limits. See article referenced later in this post for limitation. In the event you do conduct an inspection my recommendation is that they be informal and conducted with a quick walk through to ensure living conditions are safe, your housing is adequate, the landlord is fulfilling their obligations, and you are not being mistreated by your landlord. If during the course of the inspection you are found to be living in conditions that are dangerous to you or your family, the military can become involved to a certain degree. This degree varies depending on the situation and where your quarters are: on post, off post, CONUS, or overseas.