Interband absorption in ultrathin epilayers of ZnTe and ZnSe has been measured in magnetic fields up to 6 T with photon energies below and above the fundamental gap. The spectra clearly show the evolution of the 1s and 2s exciton states and of the rich structure arising from the formation of Landau levels in the continuum. The observed spectral features are analyzed using the 8 x 8 { k·p} model, which takes into account the residual strain introduced during sample preparation. From this analysis we extract highly accurate values for the energy gaps and the exciton binding energies. Effects of electron-hole correlation and resonant magnetopolaron coupling are also clearly detected in the continuum absorption. We discuss the dependence of these effects on Landau quantum number and the magnetic field by comparing the experimental transition energies with calculated ones.