IIRC, there aren’t civilian doctors and nurses at military hospitals, but it’s been a long time since I was in one.
Oh yes there are many civilian doctors and nurses, etc. at military hospitals now; my husband goes to a military hospital for treatment regularly and my oldest daughter is a civilian nurse working for DOD in an Army medical clinic. What most people don’t realize is with the volunteer military many jobs the military used to do themselves are now done by civilian DOD personnel or contractors.