All missions must be infiltrated in Long War 2.

There are other mission types, you just need to put more resistance members on intel.

Hacking, Jailbreak, Sabotage the Monument, Recover Item are all fairly common

Supply Raids and Troop Column ambushes are few and far between and occur when Advent is making an attempt to strike at your resistance havens

Liberation missions are part of a specific series that occur once you've "Found a lead" (a reward from a specific type of mission, search up "find a lead" posts for more info) that lead up to a network tower and then base assault to clear advent from a region

Retaliation mission occur only if you've failed to stop advent from reinforcing a region

Avenger Defense occurs only if you're being hunted by a UFO

Spy missions (where you kill faceless that are posing as resistance personnel) occur only if you put a soldier as a haven advisor and they detect the faceless at the end of the month. Higher rank troops are more likely to detect them. Officers are more likely to detect them as their officer rank increases. Psi ops soldiers are more likely to detect them as well.