Let us look at the system of what is occuring.
We have two black holes orbiting each other. Each black hole is its own seperate entity. Yes they are bound by each other's gravitational pull since they are in orbit. We also know a black hole is a severe local curvature of spacetime, and far out it is like any other effect. This is why if the sun suddenly just turned into a black hole, most all the planets (save perhaps mercury) would remain in their current orbits. The two black holes orbiting each other would have no way to reduce each other's gravity. In fact they don't. What happens is a state of equillibrium akin to being in the center of the earth. Gravity is pulling on you equally from two opposite directions. The vectors sum out to zero, but they do exist. If you move out towards one you'll be pulled into it. Passing between two black holes is not the same as passing through one.
If any other effects, the black holes may be a bit elongated due to tidal forces, but that is all. Eventually they will spiral into each other and the resulting event horizon will be much larger (the sum of the previous two).