Consider two supermassive black holes of equal mass orbiting about their common centre of mass. Is it the case that a free-fall trajectory along the axis of rotation would be outside of either event horizon at all black hole separation distances > 0 (based on the symmetry of the situation)?
To rephrase this, would you be able to navigate a rocket along a path at right angles to the orbital plane and bisecting the line between the two black holes with no ill effects whatsoever even when the black holes were very close to each other?
Supplementary question: What is the shape of each of the event horizons prior to coalescence?
Note: I’m assuming that tidal forces would be small until the two singularities were extremely close. Note also that the point midway between the two BHs is the L1 Lagrangian point.