We can construct a solution to this problem mathematically using geometry.
Two lines intersect in a point.
Two planes intersect in a line.
Two spaces intersect in a plane.
In all these cases, the objects in question must exist in the next higher dimension:
The two intersecting lines must lie in a plane.
The two planes must lie in a space.
The two spaces must lie in four dimension space.
Now I think we can agree that there is space both inside and outside of the TARDIS, and that they are disjoint when the door of the TARDIS is closed. In order to transit between the two spaces they must intersect, and we see transit occur when the door is open; one crosses the threshold between the outside and inside of the TARDIS by moving through the opening roughly where the door was (or slightly behind it). Therefore, the intersection of the two spaces can be seen as the plane parallel to the door's location when shut, perhaps slightly behind where it actually sits when closed.
We see this view in @SFruggiero's answer. Here was are looking through the plane of intersection and thus see the inner space through its connection to the outer space.
This implies something rather different than what some of the other answers suggest. Namely, that if the TARDIS facade was glass, you could only see the interior from one face of the TARDIS (the one where the door was). The other 5 faces (assuming the TARDIS itself was sitting on a glass platform and you could look from underneath as well) would likely appear empty and you would see straight through to the other glass on the other side. And furthermore, by varying the angle at which you look through the face containing the plane of intersection, you could actually see "behind" the area of outside space. That is to say, if you look at an angle of say 80 degrees, you can see further into the side space of the TARDIS in on direction that you can't see from straight on, and likewise 80 degrees in the other direction.
I say "likely" because we don't really know what is inside the facade in normal space. It is probably empty, because the space isn't really needed, the facade only needs to be three dimensional for the purpose of appearing consistent. However, it is also possible that there might be some machinery required for shield generation or for generating the plane connecting the two spaces. Since the entire facade dematerializes it is uncertain whether this even makes sense, as this might imply anything in this outer shell of space would need to dematerialize as well, so I suspect the entire normal space between the walls is actually empty.
Note that this solution is completely consistent with the idea (which if I recall has actually been seen in at least one episode) that anything extending further past the door on the inside can't actually be seen from the outside either. In other words, if the door is actually inset into the TARDIS control room such that some of the machinery or walls extends back on either side of the door further than the depth of the door, they do not extend into normal space; the internal space need not stop at the threshold of the door at all.
Of course, this assumes that there is only a single intersection between the space inside the TARDIS and the space outside. It is possible there are multiple intersections created: for instance, for the shields, as we have seen that the entire facade is apparently penetrable (a la Time Crash) although in my opinion the (out of universe explanation) writers didn't really think things through and realize that a lot of things about the Titanic crashing through the walls of the TARDIS as shown didn't really make sense geometrically. But to maintain the geometrically correct perspective, adding more intersections could result in multiple "windows" into the TARDIS at various intersection points, but they would all be planar surfaces giving the appearance of a "window" in normal space connecting points in normal space to the space inside the TARDIS.