(covers information from several alternate timelines)
The United Earth Military (UE Military) was the military arm of the United Earth government. The Military Assault Command Operations was a branch of this agency. Following the formation of the United Federation of Planets, the United Earth Military, along with the Military Assault Command Operations were disbanded.
In the biographical file of Captain Balthazar M. Edison, his service in the United Earth Military was noted. This file was accessed by Captain James T. Kirk in 2263 of the alternate reality. (Star Trek Beyond)