The valence-band offset at the zincblende AlN/GaN (110) interface is calculated self-consistently by means of the linear muffin-tin orbital method using up to 5 + 5 layer supercells. The value obtained is E(upsilon) (GaN) - E(upsilon) (AlN) = 0.85 eV corresponding to a type I offset. Assuming interface orientation and polytype effects on the valence-band maximum to be reasonably small, a type I offset can also be expected for wurtzite interfaces. By means of separate calculations, we also test the validity of two simplified approaches, the self-consistent dipole approximation (SCD) of Lambrecht, Segall and Andersen and the dielectric midgap energy (DME) model of Cardona and Christensen. We find that the SCD results are in very good agreement and the DME results, in fairly good agreement with the fully self-consistent results. The interface local densities of states show no indication of interface states in the main gap.