Sometimes the aliens are there but you can't see or aim at them at all. In that case, just start blowing up the alien ship inch by inch with C4, rockets, and grenades (in decreasing order of effectiveness). I have heard alien death screams but no body appears, no alien was ever seen, and no soldier could target them.
It doesn't even have to be in the alien ship. Aliens like to spawn in file cabinets and get stuck there. Just bring the whole adjacent wall down with a rocket if you can't target them directly. Although, I have only seen invisible stuck aliens in the alien ship itself, not in the rest of the map.