This question, although natural enough, is hopelessly naive. Before we can even begin to answer it we need to get some inkling of what exactly "reality" is anyway. And that is far from a straightforward question.
We could turn this question on its head and ask just how real is this familiar human realm we live in? It is a plain fact that everything we know and experience is a product of our sense organs. We never know the external world itself, but only our fabricated image of it, built up by the mind from incoming sense data. The ultimately real remains an elusive abstraction.
Some writers have tried to explain away the various realms as purely psychological states. There may be some truth to this, so long as we are consistent enough to include the present "reality" as well. It is certainly true that we can access heavenly and hellish mind-states while in the human form. But that does not at all preclude the possibility of arising after death into a more intense and inclusive form of those states.
To deny categorically the possibility of heaven and hell being, in some sense at least, real, is to be very narrow-minded. Who can say what possibilities exist within the universe? Why should the limit of the familiar be the limit of the real?
Finally, it should be noted that the Buddha himself was quite clear on this question.
Since there actually is another world, one who holds the view "there is another world" has right view. (Majjhima 60)
It is known to me to be the case, that there are gods. (Majjhima 100)
There can be no doubt of the sense in which the Buddha taught about karma, rebirth and the various realms.