I don't think any discussion about a membrane is really necessary here. What Asmita is talking about is that it feels that between his level of existence and the higher dimension above it, there's a membrane he can't penetrate. It's just a way of saying that he can't reach that level because it exists in a higher dimension, so the "membrane" is just a descriptor to say that he can't reach there unless he pierces that membrane, by rising the dimensionality of his own soul and becomes detached of the limits of time and space.
貴方のいる高次元がまるで突破できぬ薄い膜の向こうにあるようだった
It feels as if the higher dimension you were in was beyond an impenetrable thin membrane
I don't think this is meant to mean something that is literal, but rather a representation of someone from a dimension below not being able to access a higher dimension, as if there was a barrier that separated the two levels of existence. This is not something strange to think about, I have seen this same description used in other places as well and it's mostly as a metaphor to explain the difference between the two levels of existence.
Of course, sometimes there are in-between realms (Like in Platonism there's the Khôra between the physical and the metaphysical realms), but unless there's a proper explanation about those in-between realms, I don't think there's much to be discussed.
The content we already have about 8th sense users becoming unlimited by space-time and being able to percieve multiple dimensions at once is already enough to show that it's a transcendence that has physisical implications.