In doing further research...some are and some aren't depending on the agreements established with the foreign country.
Quoted an MP from another website:
"Military bases outside CONUS (continental United States) are considered sovereign American territories. Servicemen on those bases, however, are subject to the governing laws of the country they are serving in and they are called SOFA Status Of Forces Agreements. Not all American bases have these agreements though, such as installations in the Middle Eastern countries where either they havent been established or the government wont agree to or consider such measures.
There are 4 different types of jurisdictions under the UCMJ that we are taught to recognize. They are Exclusive (Federal laws only), Concurrent (Federal and state laws, or Federal and the country laws where the base is), Proprietary (dealing with property issues), and Reciprocal (meaning any military policeman from any branch of service can apprehend any member from any other branch of service for offenses committed)."