I'm not sure the EMH can be held in the brig. Couldn't he just walk through the force field or transfer his program to another room?
His mobile emitter is still a physical device, he would not be able to walk through the force field. There are no holoemitters in the brig, either. This works just fine in sickbay, though, as long as he's not wearing the mobile emitter.
In fact, on more than one occasion, he is imprisoned in a cell with no way of getting out.