interservice
adjective
in·ter·ser·vice ˌin-tər-ˈsər-vəs 
: existing between or relating to two or more of the armed services
interservice rivalry
Example Sentences
Recent Examples on the Web One received an interservice commission with the Air Force. 
Nick Anderson, Washington Post, 25 May 2018
Nick Anderson, Washington Post, 25 May 2018 Word History
First Known Use
1946, in the meaning defined above