A coupled incremental damage and plasticity theory for rare-independent and rate-dependent composite materials is introduced here. This allows damage to be path-dependent either on the stress history or thermodynamic force conjugate to damage. This is achieved through the use of an incremental damage tensor. Damage and inelastic deformations are incorporated in the proposed model that is used for the analysis of fiber-reinforced metal-matrix composite materials. The damage is described kinematically in both the elastic and inelastic domains using the fourth-order damage effect tensor which is a function of the second-order damage tensor. A physical interpretation of the second-order damage tensor is given in this work which relates to the microcrack porosity within the unit cell. The inelastic deformation behavior with damage is viewed here within the framework of thermodynamics with internal state variables.