The energy differences between In 3d5/2, In 4d5/2, and S 2p3/2 core levels are almost the same in β-In2S3, CuIn5S8, AgIn5S8, CuInS2, In6S7, and InS semiconductors. The system of these core levels provides a reference energy that can be used to put the valence band edges of these materials on a common energy scale. The experimental study shows that this common energy scale remains valid within ±0.2 eV for prediction of valence band discontinuities at heterointerfaces between these (and potentially other) indium sulfides and CuI. CuI/CuIn5S8 heterojunction showed no valence band offset and it may be interesting for applications as a diode.