One notable case where double jeopardy protections have been held to not apply at all is with acts committed by a military service member; they can be tried under both applicable civilian criminal law in a civilian court and the Uniform Code of Military Justice in a military court.
Only within certain very narrow guidelines.
Up until about 2005, the .mil routinely prosecuted active duty service members for gettings arrested and charged with a DUI. The .mil would then move to prosecute the individual at NJP before the .civ court date WITHOUT ANY FURTHER EVIDENCE other than the arrest on suspicion of DUI from the .civ authorities. They were often convicted and punished, sometimes up to and including separation from service with an OTH discharge.
ALL of that used to happen sometimes a year before the trail in the .civ courts. Even if the .civ courts acquitted the accused, the .mil punishment was already in place and there was no recourse for the service member.
After a 2005 DoD directive to commanding officers was not to do that anymore because of a series of lawsuits that challenged the authority of the .mil to try service members for violations alleged by the civil authorities, especially in regards to out of uniform/off duty/off base, on the grounds that to so, even as an NJP, was a violation of the double jeopardy protections, never mind the utter and complete lack of .mil jurisdiction!
In light of that, the DoD general order was issued "Do not get arrested/charged with a DUI". Therefore, subsequent service members who were charged were taken to NJP on "Violation of a lawful order" and double jeopardy was avoided. "Do not get arrested/charged with domestic violence" "Do not get arrested/charged with (fill in the blank)" is still the current standing general order.
DUI is not the only offense that's changed like that to avoid double jeopardy, there are lots of others that early in my .mil career I saw folks face, but towards the end the .mil had gotten out of that particular business.
For example (I've seen this happen in 2014 right before I retired), if you were to be on active duty and charged with murder by the civil authorities and taken into custody, unless it's on base (where they have jurisdiction), you'll be "Mustered in the custody of civilian authorities" until such time as you are available again for military service. Once in that muster status, the JAG will decide when you pay and benefits should be shut off, and whether to levy any other charges. Likely you'll remain on active service, until you are released from custody (even if it's only pending trail), and will stay on active duty until/unless you are adjudicated guilty and again taken into custody by the civilian authorities. From there, you can be mustered out legally.
In the event that you're cleared of all charges, that time that you were "Mustered in the custody of civilian authorities" will be added to the end of your active duty contract, effectively adjusting your end of active obligated service......but otherwise nothing changes.