Photoluminescence (PL) spectra of MBE grown short-period AlAs/GaAs superlattices with one or two enlarged wells (5 and 12 nm) have been measured at 2 K. Sharp PL peaks corresponding to excitonic transitions between the lowest electron and heavy-hole states in the enlarged wells are observed. The excitonic transition energies are calculated by means of an envelope function based model, taking into account the exciton binding energies. The model incorporates a smooth potential at the interfaces, which is represented by a diffusion potential, the diffusion length being a parameter. The calculated and experimentally observed excitonic transition energies agree well if diffusion lengths of 3.5 and 4.5 monolayers are considered in the samples with and without a buffer layer, respectively. These values are consistent with the complicated nature of the growth kinetics and mechanisms of quantum heterostructures. The PL spectra reveal also complicated structures connected with the superlattice. Their qualitative discussion confirms the smooth potential model. Thus, an attempt is made to extend the analysis of complicated AlAs/GaAs heterostructures towards real interfaces, which is essential for advanced device fabrication.