We have agreements with many countries, that military personnel, on duty, traveling in uniform, do not need a passport. Just their military ID and a copy of their orders.
If you are a military attache, RSO or MSG assigned to an embassy, you may be issued a black diplomatic one.
IF you need one to travel on official business, you will be given a reddish brown official passport.
All Military and civilian government personnel and their dependents stationed overseas can get a blue "no-fee" passport.
But you should go ahead and pay for a regular blue tourist passport, just in case you want to visit another country while off duty, for pleasure.
I used to carry several passports because you cannot use an official or fee-free passport when not on orders, and many countries won't let you enter if you have a stamp from a country they don't like. But unpopular countries such as Israel and Cuba will stamp a separate piece of paper so as not to ruin your passport.