Sadly, you can't actually change sides.
Another fun moment in the game: I had three companions following me around while I was trying to blow up a bridge. I didn't want or need them with me, but they show up on their own and won't go away. Not wanting to be ON the bridge when it came down, I used my jetpack to fly down so I could shoot it from underneath. My companions just jumped off after me. They don't have jetpacks. They survived that well enough, but then they stood around under the bridge until it fell on their heads and killed the lot of them.
By the time I reached the next bridge, three more helpers had joined me and were following me around, looking for ways to commit suicide and blame it on me.
Their deaths lower morale, and lower morale means fewer bonuses after each mission. So this foolishness does actually cost you something.
But even without the game hitting me with a fine every single time one of these dolts jumps in front of my sledgehammer, the companions just aren't that fun. Sometimes they're a bit of a help in a straight-up gunfight, but they are an incredible nuisance when you're doing demolitions. Which is the heart and soul of the game, and the one thing that sets the game apart from the ten thousand other third-person shooters out there.
(Okay, maybe a few of their deaths might have been my fault. And on purpose. And hilarious.)