(111)-oriented cubic polytypes of silicon carbide (3C-SiC) films were grown by chemical vapor deposition on 2H-AlN(0001)/Si(111) and 2H-AlN(0001)/Si(110) templates. The structural and electrical properties of the films were investigated. For film thicknesses below 300 nm, the 3C-SiC material deposited on 2H-AlN/Si presented a better structural quality than the 3C-SiC films grown directly on Si(111) using the well-established two-step carbonization–epitaxy process. The good lattice match of 3C-SiC with AlN may open a reliable route towards high-quality thin heteroepitaxial 3C-SiC films on a silicon wafer. Nevertheless, the 3C-SiC was featured by the presence of twinned domains and small inclusions of 6H-SiC. The formation of a thin AlSiN film at the AlN/Si interface is also reported. This is the first time such AlSiN layers are described within an AlN/Si heterostructure. Furthermore, noticeable modifications were observed in the AlN film. First, the growth process of SiC on AlN induced a reduction of the dislocation density in the AlN, attesting to the structural healing of AlN with thermal treatment, as already observed for other AlN-based heterostructures with higher-temperature processes. The growth of SiC on AlN also induced a dramatic reduction in the insulating character of the AlN, which could be related to a noticeable cross-doping between the materials.