Ballardian,
Yes. One side wins the initiative and takes 6 actions. Then play moves to Side 2. BUT, this doesn't mean that you have to stand still to get the crap shot out of you.
On your turn, you can set up suppression fire. If you are shot at, you can take cover even if it is not your turn.
Initiative can become extremely important if you find yourself in a bad spot at the end of the turn. You are allowed to bid action token to try to win the initiative.
And, yes, you do get invested in your the fortunes of your troops. Last game, I desperately attempted to save Irna when she got caught in the open.