From JP 3-22: Foreign Internal Defense: Participation by civilian and military agencies of a government in any of the action programs taken by another government or other designated organization to free and protect its society from subversion, lawlessness, insurgency, terrorism, and other threats to its security. Also called FID.
As has been mentioned, the "I" in FID implies that the partner nation is trying to take care of its own business, from threats that are either external or internal in origin, with help from a foreign partner (i.e. the US). If the partner nation govt is an ally of the US, and if the threat is coming from an internal source, even if it's from its own citizens, that still meets the definition of FID.

Here's a twist on what's going on in Syria. If the US actively supported the anti-Assad forces there, by supply them with weapons, logistics help, intel, basically everything short of boots on the ground, would we be then supporting an "insurgency", as defined in JP 3-22? Insurgency: The organized use of subversion and violence by a group or movement that seeks to overthrow or force change of a governing authority. Insurgency can also refer to the group itself. (JP 3-24)

Based on that definition, I think we would be, so an insurgency could be a good thing or a bad thing. Just depends on which side of the Kalishnikov you're on I guess...