You would probably need a valid military ID and you would still need proof you live in So Cal. I know a military ID doesn't have your address on it and I know you keep the ID from the state you are considered a resident of. I've got military experience, it's actually how I came to live in the wonderful state of CA.
Honestly, as a military person you are considered a resident of the state you are originally from....ie, I lived in OR and my ex-dh was Air Force, we were stationed in Nor Cal and we were not considered residents of CA, we were considered residents of OR so I don't even know if getting a So Cal pass is doable to a military person. Does that make sense? They do this pass as a way for So Cal residents to visit the parks more often, it's a perk for them. When we upgraded to our AP's we did the deluxe (now I wish we had done Premium for the adults and Deluxe for the kids) and it was well worth it IMO. We have been back to the parks 4 times since our July trip...and it would be more but we were already had plans in August and September! LOL We are going back twice in January, figuring out Feb, March and April visits too. It's well worth it to not be blacked out as much....at least for us it is.