We estimate, by reviewing the available photoluminescence data, the band alignments at heterojunctions of Zn(Cd)S(Se) semiconductors. The photoluminescence peak energies of ZnSe-ZnS, CdS-ZnS and CdSe-ZnSe strained layer superlattiCeS (SLS), with a range of well and barrier widths, have been calculated using Kronig-Penney theory and assumed values of the band offsets which yield acceptable fits to both our experiments and data taken from the literature. For ZnSe-ZnS SLS, fair agreement is obtained between calculation and experiment by assuming, in line with previous work, a negligible conduction band offset. At the same time, good estimates of the photoluminescence peak energies of CdS-ZnS and CdSe-ZnSe superlattices are obtained by assuming a negligible valence band offset in each case. We construct a band alignment diagram which predicts that CdSe-CdS and CdS-ZnSe are type-II SLs with electron confinement in the CdS layers; these predictions are borne out by experiment.