From the perspective inside a black hole: Is information about everything outside a black hole - the rest of the cosmos - represented on the inside of the (event) horizon too? NB. I realize it is the notion of a so called stretched horizon that is being used about the 2d-like sheet that information is scrambled on, but I haven't heard about its view-from-the-inside-analogy, that naively being a horizon hovering just "below" the event horizon; therefore the simplified use of "event horizon" in the question. I also realize that it would be impossible to sample (all) this information as an inside job, which I would suppose could have some bearing on the answer to the question.
I cant speak in the case of full generality, but at least for Schwarzschild and Reissner-Nordstrom (electrically charged) non-rotating black holes, there exists a coordinate system called 'isotropic coordinates'; it turns out that in these coordinate systems the 'interior' and 'exterior' regions are actually isomorphic; this means that representing the solution in these coordinates gives rise to two identical yet causally disconnected regions of space-time. These two space-times share a common boundary, namely the event horizon.
As such, the two regions can be thought of representing the same physics and the answer to your question is then a definite 'yes': the information contained within the 'interior' section also amasses on the horizon.
The Holographic Principle in Black Hole Entropy implies a radical complementarity. From the perspective of an observer outside of the black hole what falls into the black hole is thermalized on the horizon and the information is spread out on the two dimensional area of the event horizon.
From the perspective of person falling through the event horizon Leonard Susskind argues that the person does not notice passing through the point of no return but experiences the universe in 3D inside the black hole. There is a complementarity, where from one perspective an observer sees the scrambled 2D information on the surface are of the event horizon, and from a second perspective inside the black hole there is no destructive thermalization and the observer is in 3 space.
From an external perspective there is a 2D reality, and from the interior perspective there is a 3D reality, and thus we have a type quantum complementarity of exclusive realities depending on the observer.