I know that the army became desegregated during the Korean War... That would mean that the army was segregated during the Second World War.
Did black units fight along side white units during the Normandy invasion? Or the battle of the bulge? Or in the pacific theatre?
Were the black units kept in certain campaigns during the war or were they spread out?
When a person was inducted into the US Army, during World War II, they were given the Army General Classification Test. This was not an intelligence test, but was used to determine how well a person could learn and apply new information or training. The army also ranked the soldiers taking this test into five catagories. Those in Groups IV and Group V were shunted off to the Army Service Forces and not assigned to combat forces.
Due to the deplorable state of segregated pre-war education in the USA, slightly more than half of the blacks that took the AGCT were ranked in groups IV and V. The blacks that scored higher were assigned to combat units. Primarily, the 92nd Infantry division that fought in Italy and the 93rd Infantry division that did not fight together as a unit until the summer of 1945 in Luzon. The 93rd was deployed to the Pacific in early 1944, it was broken up and used as garrison troops in Bougainville, Moroitai and Saipan, before being sent to the Philippines. There was also the 2nd Cavalry division, that was only used as a rear area garrison in North Africa and a handful of independent tank and artillery battalions comprised of African American troops.
The real break through came after the Battle of the Bulge, in mid January 1945. The number of riflemen in the US Army infantry divisions that survived that battle had fallen to critically low levels. By 1945, the Army replacement system was leaving a bad taste in everybody's mouth, so the Army asked for volunteers from the rear area troops. Many Category IV and Category V rear area service troops were glad to pick up a rifle and go into action. Blacks that did so, were integrated into already existing units and no more special "all black" army units were created in 1945.
Source "There's a war to be won" chapter 25 by Geoffrey Perret