Optical spectra of type-II superlattices are presented, including Coulomb interaction and continuum states. We clarify the relative importance of above- and below-barrier transitions. By gradually increasing the band-gap modulation, we visualize the transition from a bulk semiconductor to a type-I or type-II superlattice. We show that transitions that dominate the spectrum of a type-II superlattice are absent in the spectrum of a type-I superlattice and vice versa. The interplay of size and Landau quantization in the optical absorption is studied for both a type-I superlattice and a type-II superlattice in a perpendicular magnetic field. {copyright} {ital 1997} {ital The American Physical Society}