Hexagonal boron nitride (hBN) epilayers were grown on n-type 6H-SiC substrates via metal organic chemical vapor deposition. X-ray diffraction measurements confirmed that the epilayers are of single hexagonal phase. Photoluminescence (PL) studies revealed a dominant band edge emission at around 5.5 eV, similar to the PL spectra of hBN epilayers grown on sapphire. The current-voltage (I-V) characteristics of the hBN/6H-SiC heterostructure were measured and the results were utilized to determine the band offsets of the hBN/6H-SiC heterojunctions. The analysis yielded the conduction and valence band offsets (Δ EC and Δ EV) of the hBN/6H-SiC heterointerface of about 2.3 and 0.7 (±0.2) eV, respectively, giving a Δ EC/Δ Eg value of around 76%. The measured band offsets are in reasonable agreement with values deduced from the band alignments between hBN, AlN, and 6H-SiC obtained from independent experimental data and theoretical calculations.