The physical universe doesn't actually exist, any more than a dream world does. There are probably trillions of universes in existence-- maybe infinitely many. They can't be counted, and they don't much matter because they're physically inaccessible to us. We're lucky, though, to be in an exceedingly successful universe whose laws are set ("fine tuned") to allow for complex life. The universes that don't support complex life to observe them might be "out there", but they effectively don't exist.
Mind is eternal, but the processes it can support depend on the physical system (body/brain) to which it binds, and of course that physical system evolves and, sadly, collapses. We're extremely lucky to have our minds bound to such beautiful, powerful creatures as humans. We could've just as easily been bound to cockroaches or tapeworms (and it can happen after death in a negative rebirth, but karma's another subject entirely).
The transmigration of consciousness is taken as self-evident by Eastern religions, and there's actually a fair bit of evidence for reincarnation (refer to the work of Ian Stevenson). What's controversial is whether or not a mind-- or, at least, an unenlightened mind-- can exist independent of a physical body at all. The Theravadan perspective tends to be that it cannot, whereas Tibetan Buddhists believe in an intermediate experiential state called the bardo.
Am I butterfly dreaming I'm a man? Or a bowling ball dreaming I'm a plate of sashimi? Never assume what you see and feel is real! -- Doreen, Chrono Trigger.