What branch of the military were they?

None, they were pilots for a company owned by the CIA.

Here is the link that may bring you all the answers:

http://www.air-america.org/

Here is the introduction text:

"About Air America
Air America -- "First in, Last out"

Adventure, intrigue, danger, sacrifice--words that fit Air America well. Air America was a CIA - owned and - operated "air proprietary" during the Cold War against the global menace of communism. From 1946 to 1976, Civil Air Transport (CAT) and Air America served alongside U.S. and allied intelligence agents and military personnel in the Far East, often in dangerous combat and combat support roles. Behind a shroud of strict secrecy, many Air America personnel were unaware that they were "shadow people" in counterinsurgency operations. Some 87 of them were killed in action in China, Korea, Laos, Vietnam, Cambodia and elsewhere. Though many of those Asian countries eventually fell to the communists, the contributions of Air America personnel to the cause of freedom remain unparalleled in aviation history. CAT and Air America personnel were the first Americans in China and Korea and, after the U.S. military had withdrawn from Vietnam, Air America pilots risked their lives to evacuate the last Americans. Air America -- "First in, last out."

This official website of Air America and CAT tells the 30-year story of these great Americans--shadow people, largely unknown to Americans and the world. They helped bring the Cold War to an end.

Air America -- "Anything, Anytime, Anywhere, Professionally"