In this work, we show that spectroscopic ellipsometry can be combined with photoemission spectroscopy to obtain complete interface band diagrams of non-ideal semiconductor heterointerfaces, such as interfaces between thin-film polycrystalline materials. The non-destructive ellipsometry measurement probes the near-interface band gap of the two semiconductors (including the buried semiconductor) after the interface has formed. This is important in the non-ideal case where chemical processes during interface growth modify the electronic properties of the two separated surfaces. Knowledge of near-interface band gaps improves accuracy in conduction band offset measurements of non-ideal interfaces, and it sheds light on their device physics. Both of those positive outcomes are demonstrated in the Cu$_2$ZnSnS$_4$/CdS interface used here as a case study, where the band gap of both materials decreases by up to 200 meV from the bulk to the near-interface region. This finding reveals a preferential electron-hole recombination channel near the interface, and it yields corrected values for the interfacial conduction band offset.