A computational model based on large-deformation finite element method (FEM) analysis is developed and used to evaluate the interaction between the microstructure and the heterogeneous deformation behavior of ternary composites on micro- to macroscopic scales. To uncover the influence of the plastic interphase layer on the stress—strain behavior of the three-phase system under constant strain-rate loading, the analyses of two different types of polymers with different Poisson's ratios are performed. In particular, we investigate the effects of the interphase on the normal stress at the fiber surface to predict the initiation of glass fiber—polymer matrix debonding damage. An interphase with stiffness well below that of the matrix shows a suitable effect on the micro- to macroscopic deformation behavior and suppresses the initiation of debonding, while an interphase Poisson's ratio between that of the fiber and the matrix is preferable. Furthermore, computational simulation has been performed to clarify the effects of the interphase thickness and fiber volume fraction on the normal stress at the fiber surface. The results obtained using the models suggest the realization of favorable interphase properties for suppressing the initiation of debonding at the fiber surface and improving the functionality of the reinforced polymer.