Metal matrix composites have damage for matrix cracking, fiber break and /or interfacial debonding by thermal and mechanical loads. This paper is focused on interaction between fiber break and interfacial debonding of the composite. The interface between fiber and matrix is subjected to frictional force under compressive residual stress. It gradually slips from the edge of the broken fiber during loading. A homogenization theory with multi-scale asymptotic expansion is used to solve the problem for the composite in the analysis. The displacement is expanded to macro-and microscopic fields for homogenization. And governing equations are reconstituted for each level. To solve the perturbed displacement which indicates the microscopically disturbed term, three dimensional boundary element analysis is made for a unit cell. In numerical calculation, the interfacial slip and nonlinear properties of the composite are illustrated during longitudinal loading.