Our Air Force was under command of the U.S. Army up until 1947, when it was granted separate and equal status as the U.S. Air Force, with General Henry H. (HAPPY) Arnold as it's first five star general. General Arnold was commander of the USAAC from 1938.
General Arnold was a most capable individual, and an early supporter of Britain in its efforts against the Axis. He went to England to organize the Eighth Air Force's stragic bombing against Germany, which we all know was paramount to their final defeat.
But all of that was accomplished under the auspices of the U.S. Army Air Force.