Ballistic electron emission microscopy (BEEM) measurements have been performed on Pt/p-type 4H-SiC Schottky contacts to probe the metal/semiconductor (M/S) interface and the valence band structure of the semiconductor. The Schottky barrier height (SBH) is found to be 1.45 eV, compared with 1.55 eV for Pt on n-type 4H-SiC measured under identical conditions with BEEM. A second threshold is also observed in the BEEM spectrum on Pt/p-type 4H-SiC contacts, which is possibly related to a lower-energy valence band. The sum of the measured p-type and n-type SBH's is slightly less than the 4H-SiC bandgap, which suggests the existence of an interfacial oxide layer and rather weak Fermi level pinning, consistent with prior measurements of SBH vs. metal work function.