We report an optical study of heterostructures with a type-II band alignment that are lattice matched to InP substrates grown by molecular beam epitaxy. A strong direct transition involving a confined electron and a quasibound hole state (both in the InGaAs layer) is observed in photoluminescence spectra in a low excitation regime in addition to an interface-related indirect (type-II) transition between electrons confined in the InGaAs well and AlAsSb valence band. A direct transition between the confined electrons in the first excited subband and valence band of InGaAs is also observed in a 20 nm InGaAs heterostructure in the higher excitation power regime.