The double slit experiment with either photons or electrons shows that when they are emitted from one slit, they will behave like particles and show one dot on the imaging screen, but if they are emitted from both slits simultaneously in large enough quantities, an in interference pattern will be observed. But what if photons were emitted from one slit and electrons from the other? Would you see two dots or an interference pattern?
Don't think of photons or electrons as being emitted by the slits. The photons or electrons are emitted by a single coherent source (e.g., an electron linear accelerator or a laser). The pattern that is formed on the screen depends on whether the beam from that single source passes through one slit or two parallel slits.
The idea that the single source is coherent is incompatible with it being a source of two different kinds of thing (e.g., electrons and photons).
To answer Rob's question: Uniformly illuminating one slit with a beam of electrons and a near-by slit with a beam of photons would be difficult. One would expect each to produce a single slit diffraction pattern (perhaps detected by a strip of film). The question then is: Would the EM wave packets associated with the photons interact with the wave packets associated with the electrons (also EM?) to produce a double slit pattern? That sounds like an experiment worth trying (perhaps with circular apertures).