The valence-band offsets in lattice-matched semiconductor heterostructures are calculated from first principles by means of the self-consistent, relativistic linear-muffin-tin-orbital method applied in supercell geometries. The influence of the interface structure on the offset value is examined by performing calculations for systems with ultrathin interlayers introduced at the [nonpolar (110)] interface between the two constituents. For a wide class of systems it is found that the offset is surprisingly insensitive to the inserted interlayer, although, for a given pair of heterostructure constituents, different interlayers cause vastly different charge distributions in the atomic layers close to the interface. In these cases the dipole and thus the offset remain essentially the same as for the system without interlayer. A particular, presumably small, class of semiconductor interlayers are able to affect the offset clearly. These are the semiconductors that in their bulk form introduce deviations from the ``transitivity rule'' (CuBr) in binary heterostructures.