Julia Wilbur spent time at L'Ouverture Hospital in Alexandria, built in 1864 for African American soldiers and civilians (to be precise, for non-whites, as there were a few Indian troops). She does not write about much contact with black staff members except a chaplain, Chaplain Chauncey Leonard. However, as I learned yesterday, African American women made up about 10% of the Union hospital nurse workforce.
Betsy Estilow, the president of the board of directors of the National Museum of Civil War Medicine, spoke at the Clara Barton Missing Person's Office in Washington (newly opened, run by the museum). Unfortunately, very few blacks left memoirs or other written records of their experiences but she told us the following:
About 20 to 25 black doctors treated Union troops. Three were Commissioned Medical Officers, the rest were "contract surgeons"--that is, not part of the Army (something that both black and white physicians did). One woman physician, Rebecca Lee Crumpler, worked in Freedmen Hospitals in Richmond right after the war.
Susie King Taylor is the best known African American nurse because she wrote a memoir. Read her background and the book itself here.
The jobs of cook, laundress, nurse, ward assistant, supplier, etc. often overlapped. Even so, Betsy said about 36% of cooks and 14% of laundresses were African American women.
Among nurses, whites received $12/month + rations. Blacks received $10/month + rations.