This has always been the case, and not just between civilian and military court, but between different jurisdictions:


Sometimes as difficult as determining when a defendant has been placed in jeopardy is determining whether he was placed in jeopardy for the same offense. As noted previously, the same conduct may violate the laws of two different sovereigns, and a defendant may be proceeded against by both because each may have different interests to serve. The same conduct may transgress two or more different statutes, because laws reach lesser and greater parts of one item of conduct, or may violate the same statute more than once, as when one robs several people in a group at the same time.


From:
http://caselaw.lp.findlaw.com/data/constitution/amendment05/06.html#3

>>http://www.fayobserver.com/article?id=270085
>>
>>Read to the bottom. Most here saw the miniseries and thought he may be innocent (since there wasn't ample proof to point otherwise). Now after a book deal and a miniseries, DNA proves guilty.
>
>I'm really torn about this.
>
>As a believer in the "double-jeopardy" clause in the constitution I believe that once the military cedes jurisdiction to the state it should abide by that decision. Despite the new evidence this looks like exactly the kind of double-shot the fifth amendment was designed to guard against.
>
>"No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation
>
>While the armed forces seem to be exempt from this amendment it seems to me that a strong case could be made that this is only for purposes of requiring a Grand Jury indictment for a capital crime.
>
>There are also no qualifying statements about multiple jurisdictions concerning the restriction about "twice put in jeopardy of life..."
>
>On the other hand I certainly want to see justice properly done. It certainly seems proper that, if a convicted person can receive a new trial on the basis of new evidence the "state" should have the same rights. Especially if the evidence is of a type not available at the time of the original trial (like DNA as in this case).
>
>As I said, I'm conflicted. I'll be intereted in reading other opinions.