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The transport of hot holes across metal-semiconductor interfaces is studied using ballistic hole emission microscopy. From the tip of a scanning tunneling microscope nonequilibrium holes are injected into a thin metallic overlayer on a p-type Si semiconductor, inducing a current of holes into the Si valence band. We have studied hole transport across interfaces between p-type Si and different metals (Au, Cu, and Al). It is found that the magnitude of the transmitted hole current depends strongly on the type of metal, the Schottky barrier height, and the energy distribution of the holes. In addition, we show that a significant yet smaller hole current can be induced in the reverse case where the tip is used to inject hot electrons, generating holes during inelastic decay in the metal overlayer. The results are compared to recent results on spin-dependent hole transmission in ferromagnet/p-type semiconductor structures.