Interband absorption in ultra-thin strained MBE-grown epilayers of ZnTe and ZnSe has been measured in magnetic fields up to 6 T. The spectra simultaneously uncover two effects of the magnetic field: diamagnetic shifts of exciton states, and the rich oscillatory structure arising from formation of Landau levels in the continuum. The observed spectral features are analyzed using the 8 × 8 k·p model, which takes into account the residual strain introduced during sample preparation. From this analysis we extract values for both the energy gaps and the exciton binding energies with high accuracy. Effects of electron—hole correlation and resonant magneto-polaron coupling in the continuum absorption are also discussed.