If it's by a base, the local PD *may* leave it to the command to take care of. They may pay the local fines and the like, but doing any sort of time behind the bars etc. will probably be left to the command. In my command, they'd be maxed out on a battalion level NJP minimum. Regardless of being 'government property' though, your brother-in-law has every right to press charges. If it's away from the base, they'll definitely face whatever state and local charges are brought up. There are a lot of ifs in this situation, however.
As a Marine, these things really get under my skin. Any time someone in the Corps does something wrong, the fact that they are a Marine instantly gets broadcasted out and it paints a bad picture. I've met plenty of Marines that are far from having any sort of triple digit IQ and I thing these guys should get the book, but I can assure you they are not the majority. Not that I like screwing over fellow Marines, but I'd be sure to check in with the police and see if their command was notified. This is an instance where it is certainly called for.
-Max.