Both are correct, Airforce is a synonym of Air force.
QUOTE
airforce
noun
the airborne branch of a country's armed forces [syn: air force]
QUOTE
Air Force
–noun 1. the U.S. department consisting of practically all military aviation forces, established July 26, 1947.
2. (lowercase) a similar department in any military organization.
3. (lowercase) (formerly) the largest unit in the U.S. Army Air Forces.
4. (lowercase) a unit of U.S. Air Force command between an air division and an air command.
5. (sometimes lowercase) the military unit of a nation charged with carrying out military operations in the air.
6. British. Royal Air Force.
Origin:
1915–1920