  Binary stars that are on close orbits around massive black holes (MBH) such
as Sgr A* in the center of the Milky Way are liable to undergo tidal disruption
and eject a hypervelocity star. We study the interaction between such a MBH and
circular binaries for general binary orientations and penetration depths (i.e.
binaries penetrate into the tidal radius around the BH). We show that for very
deep penetrators, all binaries are disrupted when the binary rotation axis is
roughly oriented toward the BH or it is in the opposite direction. The
surviving chance becomes significant when the angle between the binary rotation
axis and the BH direction is between \pi /4 and 3 \pi /4. The surviving chance
is as high as $\sim$ 20$\%$ when the binary rotation axis is perpendicular to
the BH direction. The angular dependence is opposite for very shallow
penetrators where coplanar prograde orbits have the lowest surviving chance (or
equivalently most vulnerable). We provide numerical fits to the disruption
probability and energy gain at the the BH encounter as a function of the
penetration depth. The latter can be simply rescaled in terms of binary masses,
their initial separation and the binary-to-BH mass ratio to evaluate the
ejection velocity of a binary members in various systems. We also investigate
the disruption of coplanar, eccentric binaries by a MBH. It is shown that for
highly eccentric binaries retrograde orbits have a significantly increased
disruption probability and ejection velocities compared to the circular
binaries.
