If you are a service member who is arrested for DUI while on base, your commanding officer will have a large role in determining what will happen to you. He or she can do anything from determining that you should only be subject to an administrative action to levying an Article 15 non-judicial judgment to recommending a court martial. Both an Article 15 and a court martial fall under the Uniform Court of Military Justice.
Although military service members won't face criminal charges in civilian court if their DUI arrest was on base, they may still be subject to other limitation of their driving privileges by the state. These can include having their license suspended or the requirement of an ignition interlock device on their vehicle(s).
Service members who are charged with DUIs while off the base, however, can face civilian as well as military court processes. The two jurisdictions may consult to determine where the service member will be tried. Even if you are acquitted in a civilian court, you can still be subject to punitive actions, including court martial, in military court.
In some cases, civilians (usually civilian employees or friends or family of service members) are arrested for DUIs while driving on a military base. Those cases are handled in federal court. However, state DUI laws will still apply since civilians are subject to federal DUI laws.
If you are a member of the military and/or have been charged with a DUI on a military base, it's advisable to consult an attorney with experience in military law. He or she can help you deal with both military and civilian courts.
Source: FindLaw, "Military DUI: Court Martial and Civilian Charges," accessed March 24, 2016