As the Attacker you may only take casualties from the active Power. As a defender, with multinational forces, all defending units fight and can be taken as casualties.
From the 1914 Rulebook (page 17)
Phase 3: Conduct Combat
Combat occurs when your units share the same space with units belonging to one or more opposing powers and you decide to commit your units to an attack. Only enemy units may be attacked. When attacking, all units in the space belonging to your power must attack. You are required to attack only in territories that have become contested this turn due to your movement of units into them. Attacks in territories that were already contested at the beginning of the turn and in sea zones are always optional, even if you have moved units into them this turn.
Only one power can attack while in a sea zone or contested territory, but all enemy forces that may be present in such a territory must defend together (see “Multinational Forces”, page 22). Players must always defend with all units in the space if attacked.