A flyby of orbiting supermassive black holes 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.
 A: You can't have a stable configuration of two orbiting black holes at all separations.  Even in the case of a test particle orbiting a single non-spinning black hole, the innermost stable orbit for the test particle is located at $r=6M$, with closer orbits plunging into the hole (circular orbits closer than $6M$ are unstable solutions analogous to balancing a rigid pendulum vertically.)
If you have two black holes of appreciable mass, they will radiate away energy, gradually falling in closer and closer to each other, and then at some time before a common horizon is formed (also meaning before the "center of mass" of the system is inside the horizon), the two holes will hit their last stable orbit, and then will very rapidly combine, giving off a large burst of radiation, and an eventual end state of a single black hole.  
As a final aside, I should note that a spinning black hole's singularity is a ring, not a point, and that the center of this ring IS locally flat.  Since a binary black hole collision will definitely have net angular momentum (even if just from the orbital angular momenta of the holes), this means that the end state will almost certainly be a spinning hole, so it is not necessary that the "center point" ever not be locally flat.
A: As I understand this question the two Black Holes initially have some distance D between their Event Horizons, a region of Space also containing L1. So yes I think that this journey outside the Event Horizons is theoretically possible assuming that they dont coalesce on you whilst on this journey.
One practical problem, and hence risk, likely arises from the non-stability of L1 (at least in Newtonian 3 Body theory - I assume also true in General Relativity). This would mean that a journey which slightly deviated from it, could orbit the nearest BH (in Newtonian theory tangentially escaping the system is more likely). So determining the exact nature of this instability for GR for this setup is crucial. 
Once orbiting a Black Hole - even although outside the Event Horizon - the next issue is whether your Spaceship has the energy to escape that orbit. Meanwhile with the two Black Holes converging around you there could still be problems staying out of one of the Event Horizons....
I should point out that whilst researching this question, I have come across the "Interplanetary Transport Network" - http://en.wikipedia.org/wiki/Interplanetary_Transport_Network
A: Even before the horizons merge to form a common horizon, the tidal forces may be very large, even for supermassive BHs. For a single black hole, particles originating from outside the BH cannot get closer than something like 1.5 times the horizon radius without getting captured. So a particle or photon that gets slightly closer to one of the two BHs would get captured. Thus, if you try to "thread the needle" you might get split in two.
For a picture of the shapes of the horizons, see http://arxiv.org/abs/gr-qc/0610122 Fig 1.
A: 
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?

I can't see how you would do that with two neutron stars let alone two black holes.
The electromagnetic field is extreme, growing to 10$^{16}$ times that of Earth. Is your rocket non-magnetic; what about the electronics on board. There's a long of interaction between the two objects prior to their collision, a fight to see whom can rip the skin off of the other.

Here is a NASA Goddard video showing the results of 6 weeks of supercomputer time used to model the last few microseconds of their life and the events leading up to it: https://www.youtube.com/watch?v=ow9JCXy1QdY or a simulation showing density on the left and magnetic field on the right: https://svs.gsfc.nasa.gov/vis/a010000/a010700/a010740/3mag.bns.01.mov and https://svs.gsfc.nasa.gov/vis/a010000/a010700/a010740/jetformation_02_med.mov .
More info about the modeling of this event is on this webpage: "The engine that powers short gamma-ray bursts", for high resolution stills see: "When Neutron Stars Collide", and an earlier paper: "On the black hole species (by means of natural selection)" where the author explains that the exact topology of multiple black holes in higher dimensions is not well understood.
A: 
What is the shape of each of the event horizons prior to coalescence?

The function is called pair of pants, see reference 1 and reference 2, which basically looks like this:


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?

If this is your assumption: 

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.

then yes, of course. As long as you stay outside of the horizons you surely can escape.
