United States Military Should the word "military" be capitalized here?

No.

The United States is a proper name and should be capitalized. But the military is just something it owns.

No. Being generic, the term "military" needs no capital - and nor does "Armed Forces".

(https://en.wikipedia.org/wiki/United_States_Armed_Forces relies solely on the wholly ambiguous "armed forces - Capitalize only as a proper name (Armed Forces Day) or part of a title or when preceded by U.S., as in U.S. Armed Forces" at https://www.navy.mil/submit/navyStyleGuide.pdf

(That Wiki… mentions no "armed forces" in explaining the US national command structure and seems unclear even whether the Marine Corps stands alone or is part of the Army or Navy.)

(With apologies to those who see this as disdainful, why should your editor get away with that vacillation? With the best will in the world, grade school should have explained the difference between proper and improper, or common, nouns; high school should have provided the research skills to check either in a paper reference library, or on the internet, to which category "military" belongs.)