I meant the United States military during World War 2, not the Army itself.
That's awfully specific in some ways, too generic to answer in other ways. What army? In what era?
Something like this may have happened once or twice, but on the level of policy, the US Army kept black soldiers and white soldiers separate from each other until the military desegregated in 1948. Prior to 1944, black soldiers served in segregated units at the battalion, regimental, and even divisional level, such as the 92nd and 93rd Infantry Divisions. Though some were combat troops (especially artillerymen and tank destroyer crewmen), the majority of black soldiers served in support units, driving trucks, unloading ships, and maintaining and improving roads.
The shortage of white combat troops in Europe in late 1944 led to a small but interesting experiment with black combat troops serving in overall white units. About 2,000 black soldiers, some of whom were non-commissioned officers, volunteered to undergo infantry training and join white units. They were not interspersed individually, but inserted as entire platoons of ~60 men, with white officers and (usually) white NCOs in command. Training began in January 1945 and lasted until the end of February, at which point the 53 colored platoons were dispersed to various infantry and armored divisions, where they would serve side by side with white platoons. By all accounts the black platoons acquitted themselves well.