Let's say a black hole of mass $M$ and a very compact lump of anti-matter (not a singularity) also of mass $M$ are traveling toward each other. What does an outside observer see when they meet?
Will they blow themselves apart in a matter/anti-matter reaction? Or will their masses combine, never quite meeting in the infinite time dilation at the event horizon?
Whether the infalling material is matter or antimatter makes no difference.
Fundamentally, the confusion probably comes from thinking of black holes as normal substances (and thus retaining the properties of whatever matter went into making them). Really, a black hole is a region of spacetime with certain properties, notably the one-way surface we call an event horizon. That's it. Whatever you envision happening on the inside of a black hole, whether it be a singularity or angels dancing on the head of a pin, is completely irrelevant.
The reason spacetime is curved enough to form an event horizon is essentially the due to the density of mass and energy in the area. Antimatter counts just the same as matter when it comes to mass and energy. Anti-protons have the same, positive mass as normal protons, and at a given speed they have the same, positive kinetic energy too.
Even if you wanted matter and antimatter to annihilate somewhere near/inside a black hole, the resulting photons would cause no less curvature of spacetime, as all particle physics reactions conserve energy and momentum. This is related to how you could form a black hole from nothing but radiation.
What might possibly be unintuitive is that during matter-antimatter annihilation nothing disappears - the particles simply get converted to other particles and energy. From the point of gravity, however, energy is mass - so from the point of an outside observer, if no particles escape the system, then it doesn't matter if the annihilation reaction happened or not - the total mass=energy of the system doesn't change.
To add just a little to what Chris has said, when the antimatter falls into the black hole - let's say it's a positron - it annihilates with regular matter. In this case, the positron would presumably annihilate an electron, creating two gamma rays (very high energy light) of energy 2*(0.511 MeV). Just as matter cannot escape a black hole, photons (our gamma rays) can't either. Spacetime is so curved that they have no path out! So, essentially, the mass-energy of the anti-matter can't escape, even if it turns into 'massless' photons.
Curved spacetime causes other interesting effects, including gravitational lensing where large objects like galaxies or stars bend the path of light passing nearby them.
