Quote:
10 U.S. Code § 101 - Definitions
(4)The term “armed forces” means the Army, Navy, Air Force, Marine Corps, and Coast Guard.
That's direct from US Code and is the definition of "armed forces" or in common parlance "the military." They are the only branch of the military that does not fall under the operational control of the DoD, which doesn't affect their status as a branch of the Armed Forces. Members of the Coast Guard are entitled to the same pay rates and benefits as members of the DoD branches of the military.