The valence-band offsets in 15 lattice-matched semiconductor heterostructures are calculated from first principles by means of the self-consistent, relativistic linear-muffin-tin-orbital (LMTO) method applied in the supercell geometry. The outermost cation d-like states hybridize with the valence-band maximum, and they influence therefore the offset values. Their most important effect, however, is to modify the self-consistent potential as compared to calculations treating these states as atomiclike (``frozen'') core states. They must therefore be included as fully relaxed band states. The effects of the size of the supercells are analyzed, and it is found that, although the charge redistributions occur over at least three layers, a 5+5 cell is usually sufficiently large to give a reliable offset value. CdTe/HgTe represents in this respect an exception, and this system is one case (HgTe/InSb, CdTe/InSb, and InAs/GaSb being other examples) where an ``anomalous'' charge transfer is found. This anomaly is associated with confinement at the interface. Interface dipole effects are analyzed, and it is demonstrated that they in many cases tend to drive the systems towards a lineup of ``charge-neutrality'' levels.