There is another way to do it, but it's going to be quite difficult:
You have 2 regions, at the start and the end of the bridge, the bridge itself isn't actually a bridge, just a doodad with no pathing and the bridge model.
Then you put flying pathing blockers on the sides of the bridge, but not on entrance/exit.
Then you need to make a trigger to give units that try to cross the bridge storm crow form and the correct height of the bridge.
If done correctly, the units will appear to be walking on the bridge while they're actually flying over it, and since the bridge has no pathing, units will be able to walk under it.