My understanding is that Germany had no policy towards black combatants and POWs in WW2. However, this did not mean that they were treated equally to white POWs. Records show that sometimes German soldiers wouldn't take black soldiers prisoner. Most notably, there is an incident that happened in Wereth, Belgium were 11 black American troops were probably killed when captured by German SS troops rather than being taken prisoner at the Battle of the Bulge. Even when taken prisoner, they were not treated the same as white POWs. They were kept segregated from whites for the most part. Conditions were considerably worse. Among French colonial troops, over half died while being POWs.

The Tuskegee Airmen are an interesting group to look at for this. They were all black Americans, 32 of whom were captured.

Alexander Jefferson (possibly one of the most famous of these men) talks about being captured in a very similar way to that of other white POWs. In an article about his experience he states that he had very little to do with the Germans as this was the role of the camp's Man of Confidence, but states that "I was treated as an officer and a gentleman" (he was considered a Non Commission Officer (NCO) and above, so would have been placed in flight crew specific camps (Stalag Lufts), or Officers' camps (Oflags).)

On page 70 here you can see that treatment was pretty awful for flight crew. They were considered to be preying on women, children, and civilians and therefore often received truly awful treatment.

Although the Wikipedia article does mention the segregation of some black French soldiers, I haven't found much in the way of reference to this occurring with US, or British forces in my studies on the topic. I have checked the sources for this, and cannot find much to go on. There are examples of attempted segregation of Jewish troops which are mentioned in a lot of POW logs - however often the POWs in the camps attempted to stop this happening. In Stalag 383 the Palestine Pioneer Corps were strongly integrated.

I cannot say for certain either way, but remember that a POW does not become classified as such until they are registered at a camp. Until this point they represent a danger, as well as someone who has just been trying to kill you. Therefore it was not uncommon for surrendering troops to be shot regardless of the Geneva Convention etc. However, in specific reference to the Tuskegee airmen Jefferson mentions more issues with American troops' racism, than with that of his captors.