The properties of ultrathin (1–2 monolayer) (hydroxy)oxide films on transition metal substrates have been extensively studied as models of the celebrated Strong Metal–Support Interaction (SMSI) and related phenomena. However, results from these analyses have been largely system specific, and limited insights into the general principles that govern film/substrate interactions exist. Here, using Density Functional Theory (DFT) calculations, we analyze the stability of ZnO_xH_y films on transition metal surfaces and show that the formation energies of these films are related to the binding energies of isolated Zn and O atoms via linear scaling relationships (SRs). Such relationships have previously been identified for adsorbates on metal surfaces and have been rationalized in terms of bond order conservation (BOC) principles. However, for thin (hydroxy)oxide films, SRs are not governed by standard BOC relationships, and a generalized bonding model is required to explain the slopes of these SRs. We introduce such a model for the ZnO_xH_y films and confirm that it also describes the behavior of reducible transition metal oxide films, such as TiO_xH_y, on metal substrates. We demonstrate how the SRs may be combined with grand canonical phase diagrams to predict film stability under conditions relevant to heterogeneous catalytic reactions, and we apply these insights to estimate which transition metals are likely to exhibit SMSI behavior under realistic environmental conditions. Finally, we discuss how SMSI overlayer formation for irreducible oxides, such as ZnO, is linked to hydroxylation and is mechanistically distinct from the overlayer formation for reducible oxides such as TiO₂.