The exact band alignment at organic/inorganic semiconductor heterojunctions is influenced by a variety of properties and is difficult to predict. For organic/inorganic bilayer heterojunctions made of poly(3-hexylthiophene) (P3HT) and n-type 6H-SiC, the band alignment is determined via current-voltage measurements. For this purpose, a model equivalent circuit, combining thermionic emission and space-charge-limited current effects, is proposed which describes the behavior of the heterojunction very well. From the fitting parameters, an interface barrier height of 1.1 eV between the lowest unoccupied molecular orbital (LUMO) of P3HT and the conduction band (CB) of 6H-SiC is determined. In addition, from the maximum open circuit voltage of 6H-SiC/P3HT diodes, a difference of 0.9 eV between the highest occupied molecular orbital (HOMO) of P3HT and the CB of 6H-SiC is deduced. These two values determine the alignment of the energy bands of 6H-SiC relative to the HOMO and LUMO of P3HT. The 6H-SiC/P3HT bilayer heterojunction exhibits an open circuit voltage of ~0.5 V at room temperature, which makes such a materials system a potential candidate for bulk heterojunction hybrid solar cells with 6H-SiC nanoparticles.