He left out the carrying arms openly part.
"Insurgents" as in Iraq tend to hide their weapons behind clothing or other objects so as to appear as unarmed civilians until such a time as they spring their traps; they deliberately select firing positions from within crowds of unarmed people of all sexes and ages so as to prevent themselves from standing out in a crowd. Or they simply hide their bombs in objects designed to look civilian. They don't put their insignia or other identifying marks on car bombs.
US civilian contractors carry their arms openly, do not select firing positions inside crowds of civilians for their ambushes, and do not use civilians to protect themselves by taking advantage of the enemy's reluctance to kill civilians.
The last one is a no-brainer since none of our enemies have any reluctance to kill civilians.
Citizen militias are expected to carry arms openly and not fire from beneath the skirts of women or from inside schools and churches and mosques simultaneously occupied by noncombatants. Even if uniforms are unavailable they are legitmate combatants so long as weapons are carried openly.
Specifically, which Geneva Convention states that? The Convention linked to in a previous post simply defines 'Prisoner of war', and the protections of those prisoners.
I have yet to find any Geneva Convention which even uses the term 'lawful combatant'.
"Under Geneva to be considered a lawful combatant- either civilian militia or military, you must wear a uniform OR identifiable insignia, or be carrying arms openly to set yourself apart from unarmed civilians."
No. It's not "or." They have to fulfill all of those requirements and more:
Geneva Conventions
(2) Members of other militias and members of other volunteer corps, including those of organized resistance movements, belonging to a Party to the conflict and operating in or outside their own territory, even if this territory is occupied, provided that such militias or volunteer corps, including such organized resistance movements, fulfil the following conditions:[ (a) that of being commanded by a person responsible for his subordinates; (b) that of having a fixed distinctive sign recognizable at a distance; (c) that of carrying arms openly; (d) that of conducting their operations in accordance with the laws and customs of war.
http://www.globalissuesgroup.com/geneva/convention3.html#4