In this study, a coarse-grained model is developed to describe the interatomic interactions between a cross-linked epoxy and a copper substrate. Based on this model, the tensile deformation and failure of an epoxy/Cu bimaterial is studied. Attention is given to the microstructural evolution near the epoxy/Cu interface, and its effects on the overall stress-strain behavior of the bimaterial. It is found that, under uniaxial strain, plastic deformation in the epoxy/Cu bimaterial is localized to a thin layer of epoxy next to the epoxy/Cu interface. This discovery enables the definition of an interfacial zone. Consequently, a macroscopic cohesive zone model can be constructed at the continuum level where the separation of the interface is given by the stretching of the interfacial zone in its thickness direction.