That's what I was told at Bragg, by a 1SG. That if the civilian spouse answers the door then the answer is NO. They cannot force a civilian, off post, to do anything.
Reference for these regulations will not be found in an AR, but in the manual for courts martial. Military Rule of Evidence 313-315 covers inspections and searches
As for off post housing, military commanders have no authority to authorize a search or inspection. See military rule of evidence number 315. It states explicitly who may authorize what searches. Competent military authority is limited to authorization of searches of military property. Civilian owned property located off of a military installation requires a civilian search warrant.
Official Regulation:
Rule 315. Probable cause searches
(a) General rule. Evidence obtained from searches
requiring probable cause conducted in accordance
with this rule is admissible at trial when relevant and
not otherwise inadmissible under these rules.
(b) Definitions. As used in these rules:
(1) Authorization to search. An “authorization to
search” is an express permission, written or oral,
issued by competent military authority to search a
person or an area for specified property or evidence
or for a specific person and to seize such property,
evidence, or person. It may contain an order directing
subordinate personnel to conduct a search in a
specified manner.
(2) Search warrant. A “search warrant” is an express
permission to search and seize issued by competent
civilian authority.
(c) Scope of authorization. A search authorization
may be issued under this rule for a search of:
(1) Persons. The person of anyone subject to military
law or the law of war wherever found;
( 2 ) M i l i t a r y p r o p e r t y . M i l i t a r y p r o p e r t y o f t h e
United States or of nonappropriated fund activities
of an armed force of the United States wherever
located;
(3) Persons and property within military control.
Persons or property situated on or in a military installation,
encampment, vessel, aircraft, vehicle, or any other location under military control, wherever
located;
You can read the regulation in full at
http://court-martial.com/Media/military-rules-evidence.pdf under rules 313-315 pages 12-15.
I am sure there are different scenarios but these are the official regulations regardless.