Bonjour Patrick,
At the time, black soldiers did serve in the US Army. However, they served in segregated units with harsher living conditions and some of the worst assignments.
The US Marine Corps had a different policy. The USMC was all white until June 1942. The newly created WWII unit, a 900 man defense battalion, was segregated.
Full racial integration of the US Armed Forces did not occur until President Truman ordered the change. Generally speaking, integration did not occur until after the Korean War.
There are some technical exceptions to all of the above that military historians get involved with, but basically, ....the US military was segregated.
Saluations,
BobW