The interaction in the show between civilian and military groups was actually one of the things that intrigued me the most about the show.
There were times I thought Roslin should have been pushed out an airlock for some of her ideas, and then there were one or two times I thought she made sense.
To me, when you believe you have 50,000 humans remaining from billions, and are being hunted -daily- by the beings who want to extinguish your race, I believe that the military would establish marshal law, and any civilian ships who didn't like it would be welcome to take their chances on their own. To me, the show went a bit too far with the non-military leaders trying to keep their 'freedom' and avoiding letting the military do its job. In peacetime, I'd agreed with Roslin's choices most of the time. But on the verge of extinction? Let the people trained for war do the protecting without red-tape and other silliness.
It was interesting to see their take on it, though.
As OM said, each side of the equation probably has a fairly straight-forward command structure: definitely obvious for the military, but less so for the civilian side. It's when you mix the two that things become even more interesting! :)