A Heavy soldier with both the Suppression and Mayhem skills does AoE damage around the target when using Suppression.
Does this damage apply to all units in the area, or only to enemies?
The answer is: No, the Suppression AoE does not affect friendlies.
I tested by moving a friendly unit next to an enemy and using Suppression, with Mayhem and a Heavy Plasma. The (robotic) enemy took 6 damage, and the friendly none.