We have studied the electronic structure of the interface between 6H-SiC{0001} and graphite. On n-type and p-type 6H-SiC(0001) we observe Schottky barriers of Phi_b,n^Si= 0.3+-0.1eV and Phi_b,p^Si=2.7+-0.1eV, respectively. The observed barrier is face specific: on n-type 6H-SiC(000-1) we find Phi_b,n^C=1.3+-0.1eV. The impact of these barriers on the electrical properties of metal/SiC contacts is discussed.