I think most theories of mind, including Cartesian dualism, accept the existence of some sort of mind-independent material world while also saying that this world is experienced by a non-physical mind. Descartes believed that the mind interacted with the brain by way of the pineal gland, while Gottfreid Leibniz believed that the body and the mind didn’t interact at all, but moved in perfect concert because they had been set in motion to do so ahead of time by God.
Then there’s Sartre, who distinguished not between mind and body but between essence and existence, with essence being essentially that which is self-aware and can think and feel, and existence being everything else.
My own view is materialist, but I suppose I cheat a little by suggesting that the fact that we have the phenomenological experience of possessing a non-physical mind is deeply significant. I see the mind as sort of a metaphorical concept used to describe our experiences, and if you take that a step further I think you could call a person “that which experiences itself as having a mind.”
Incidentally, I’m loving answering these philosophy questions. If you guys have got any more you’re curious about, keep ‘em coming.