I did some Googling, and here is a link to the uniform regulations permitting the use of religious headgear:
http://www.deomi.org/DiversityMgmt/RelHeadgear.cfmReligious Headgear
Army
AR 600-20 (Army Command Policy), Section 5-6, paragraph g(4)(d), lays out the required criteria for the wearing of religious headgear.
Note that paragraph g(4)(d)5 states:
"Religious headgear that meets these criteria is authorized irrespective of the faith group from which it originates."
The Jewish yarmulke is specifically approved for wear by military personnel, in accordance with DODD 1300.17; personnel of other faiths who wish to wear religious headgear should consult first with unit leaders and/or Army legal authorities.
ARMY REGULATION 600-20
Navy
SECNAVINST 1730.8B (Accommodation of Religious Practices) provides very general guidelines regarding headgear (see paragraphs 10b-k), although the permissibility of the yarmulke is addressed specifically in paragraph 10.e.
SECNAVINST 1730.8B
Marine Corps
MCO P1020.34G with changes 1-4 (Marine Corps Uniform Regulations). See Section 3005 (Caps/headgear), addressing the wearing of headgear during religious services.
MCO P1020.34G
Air Force
AFI 36-2903 (Dress and Personal Appearance of Air Force Personnel)
Table 2.6 (Clothing/Accessory Standards), Item 15, provides guidance on who may approve religious headgear, as well as color and concealing requirements.
Table 2.9 (Religious Apparel Waivers) outlines the waiver submission and approval process.
AIR FORCE INSTRUCTION 36-2903
Coast Guard
On 9 Jan 2007, the Commandant of the Coast Guard issued an ALCOAST (Subject: Results of Uniform Board No. 41), in which the wearing of religious headgear by Coast Guard personnel is permitted. The type of headgear (i.e., pertinent faith group) is not specified. The Jewish yarmulke is specifically approved for wear by military personnel, in accordance with DODD 1300.17; personnel of other faiths who wish to wear religious headgear should consult first with unit leaders and/or Coast Guard legal authorities
UNIFORM REGULATIONS, COMDTINST M1020.6 (SERIES)