What makes a military commission military?

Carol Rosenberg's Miami Herald article about the government's appeal of Judge Vance Spath's order abating the Nashiri military commission trial notes that the lead prosecutor for that case is on loan from his usual employment as an Assistant United States Attorney in the Eastern District of Louisiana.

As those who follow the case know, there have been several civilians on the defense side, although they have withdrawn. And until he was removed (for reasons that have still not been revealed), the convening authority, Harvey Rishikof, was (like one of his predecessors, Susan Crawford) a civilian. Being a court-martial convening authority is ordinarily an attribute of military command (the codal exceptions being the President, who is commander in chief under the Constitution, the Secretary of Defense, and the service secretaries), but in the case of the commissions convening authority, only the convening authority attribute exists and not the fact of command, akin to the smile of Lewis Carroll's Cheshire Cat.

To be sure, the presiding judge is a military officer, and the commission's members will be if and when the Nashiri case ever goes to trial, but at a certain point it seems fair to ask whether this is in substance a military institution or whether its military character has been so diluted that it is only a legal trompe l'oeil.