We report ab initio calculations of the electronic structures and the band line-ups of heterocrystalline superlattices (HSLs) , and (n = 1,2,3). The band line-ups at both the (3C-BN)/(2H-BN) interface and the (3C-SiC)/(2H-SiC) interface are found to be type II, with valence-band offsets of 0.16 eV and 0.14 eV and conduction-band offsets of up to 1.56 eV and 1.08 eV respectively. For the (3C-GaN)/(2H-GaN) interface, the valence-band offset is found to be almost zero, and the conduction-band offset is about 0.4 eV. It is found that the band gaps in the HSLs decrease rapidly with the increase of the slab thickness. This `abnormal' band-gap behaviour is shown to be due to the internal electric fields induced by the spontaneous polarizations in the 2H structures.