This is the (one of the) difference(s) between property and substance dualism.

You can claim that mental properties and physical properties interact without claiming that they are ontologically the same thing, or that one supervenes on (i.e. is just a result of the behaviour of) the other.

There are ways around the problem of interaction for substance dualists too, but they often rely on ad hoc interventions like God guaranteeing that the two worlds always match up (occasionalism).