Yeah, Preferred Enemy (anything other than a Faction) was always weird.
As you've stated, the
FAQ tells us that multi-Faction units count as all of the Factions involved, so we take a logical step and apply that to non-Faction attributes.
Taking it even further, the challenge is considered ongoing until the end of that fight sub-phase even if one or both combatants die (p102), although for the purposes of a specific part of the challenge rules (Outside Forces), it could be argued that so as long as your unit still contains a character (from CoF) and the enemy unit contains a character, you get to keep
PE.