This paper investigates the effects of thin plastically deformable layers embedded in an elastic coating upon debonding of a multilayer from its substrate. Such coatings are normally deposited at high temperature and cooled to ambient, resulting in significant stresses from thermal expansion mismatch. Other stresses can develop during subsequent thermal cycling if volumetric changes such as phase changes or oxidation occur in the system. We present an elastic-plastic model to calculate these stresses in the adhered state (after deposition and cooling but before debonding) and the released state (after delamination). These results are used to calculate the steady-state energy release rate (ERR) that drives debonding at the interface between the multilayer and the substrate. It is shown that plastic straining in the ductile layers can lead to significant reductions in crack driving force by dissipating energy both before and during coating release. Regime maps are developed to illustrate reductions in ERR in terms of the yield strength and volume fraction of the metal layers. As an example, the model is used to predict the impact of embedded platinum layers within an yttria-stabilized zirconica coating; the crack ERR for the composite coating is shown to be 30% lower than that for a uniform ceramic coating.