WARNING: Philosophy ahead.
Well, if heaven is described as being in the presence of God, then there is something in there that suggests that the "spiritual realm" may be from the same substance that God is of. So, I think it would be fairly logical to say that the spiritual realm could be God creating it from his own substance. However, it doesn't necessarily have to be the case.
The main problem that arises in a dualistic substance theory is the interaction between the two substances. This is classically seen in the mind-body problem. If the mind is a separate substance from the body, how does it communicate with the body? Answers have ranged from:
1. There is only a physical substance. This is can be monism (the mind is reducible to physical states), property dualism (mental states can't be reduced, but still one physical substance). This is a decent answer, but in the context of Christianity, we must reject the answer because it denies the dualism of body and soul. It could still work for someone who believes in supernatural creation though, if they were to be a deist.
2. There is some sort of currently unknown process where the mind communicates to the body. Descartes, who came up with this idea, said it happened in the hippocampus I believe. This is bad because all the evidence we have about neurology disagrees, and Descartes was pretty much just making up stuff at the point when he decided to use the hippocampus.
3. There is no physical substance, only mental. Anything physical is a perception created by the mind. This is idealism. This is bad because how do all humans, with their own mental perceptions, interact with each other in a unified fashion?
4. Somewhere between the two extremes of idealism and monism. This is Kant's theory of transcendental idealism, where the mind brings the perceptions of space and time to the table, but we exist in some sort of world. However, since we are beings of time and space, we can't know what the world is really like. This world is referred to as the noumenal world, and the world we perceive the phenomenal world.
So the problem with our two separate substances (physical and spiritual--our universe and heaven) is: how does God and other spiritual creatures such as angels, whom are of a completely different type of existence, interact with our physical world? We could chalk the answer up to "God is infinitely powerful!" but I don't think that's a very satisfying answer.
My own personal theory is that the creation basically has a number of external "dials and buttons" God can turn or press. That's a terrible analogy, but basically the bridge between the physical and the spiritual realms is facilitated by God tinkering with unknown external things that themselves cause physical changes. They are gateways, so to speak, from the spiritual to the physical. Angelic appearances and the like would all rely on these unknown "spiritual movers" to interact with our world. So, the appearance of an angel in this world is fundamentally physical, despite their substance being spiritual.
The problem with that theory, though, is that it shifts the burden of substance interaction to these "spiritual movers." They are gateways from outside the creation into the creation, but how do they actually work?
Expanding on the idea I presented above, it could be said that each person's spirit is one of these spiritual movers or gateways. This may be the point at which the human inability to comprehend certain things about the divine arises. We can say that the soul/spirit, which is somehow connected to the body, facilitates interaction with the divine (such as the holy spirit dwelling within us), but we cannot say how that process is accomplished.
Because of our perceptions as beings of time and space, we are fundamentally unable to see how this could possibly work. The spiritual movers would be a part of Kant's noumenal world--although the notion of us being able to reason our way to the existence of these spiritual movers or gateways would be beyond the limits that Kant himself placed on the noumenal world.
So perhaps Kant's noumenal world isn't as restrictive as he thought it was, OR I'm just horribly wrong.

Probably closer to the second choice.