I got lawyers guns and money. Handle this x)
I've actually got half a notebook of musings on this very subject. The way I imagine it, marines and army would most likely form "outposts" of sorts. Shotwave communications linking them incredibly loosely, divided by geography and former population density. The fleet (i'm in the Navy) would get much leaner. Probably eliminate females from the service altogether. No BS tolerated - endanger the mission = walk the plank kinda discipline. Probably have zero use for the sub fleet, or nuclear carriers. Easier to raid fossil fuel supplies that are laying dormant and train surivivors on diesel engines than it would be to train nuclear engineers. So we'd switch to 4~ diesel dependency and have to take what we needed.
I envision the center of whatever government there is being based on islands. The the "forward outposts" being places such as Coronado in San Diego. Easier to take an island than an inland mass. then fortify it. clean-sweep of the perimeter daily with soundless weapons. From there, loose coordination with whatever joint service outposts existed could be coordinated. But honestly, overall, I imagine we do only marginally better than the better organized civilian factions. But yes, a little better.
"You don't gotta believe in your government to be a good citizen.. You just gotta believe in your country."
I would probably try and take the SF route, of sorts. Instead of shacking up and trying to hold back the hordes of undead, I would rather travel with a small group of my military brethren (I could give a shit what branch) and find the small pockets of humanity surviving among the dead. I would train them up as best as possible, and instruct them on where to go to find military outposts. The outposts would get bigger, but with more mouths to feed comes more bodies for defense. Along the way, slowly and methodically remove the enemy. The people are the true hope for rebuilding humanity, but we servicemen cannot babysit them.
"Give a man a fish and he will be full for a day. Teach a man to fish and he will never go hungry."