We report on first-principles calculations of multilayers of zinc-blende half-metallic ferromagnets CrAs and CrSb with III-V and II-VI semiconductors, in the [001] orientation. We examine the ideal and tetragonalised structures, as well as the case of an intermixed interface. We find that, as a rule, half-metallicity can be conserved throughout the heterostructures, provided that the character of the local coordination and bonding is not disturbed. At the interfaces with semiconductors, we describe a mechanism that can give also a non-integer spin moment per interface transition atom, and derive a simple rule to evaluate it.