In order to investigate the behavior of elastoplastic composites exhibiting both isotropic and nonlinear kinematic hardening, we extend the Double Incremental Variational (DIV) formulation of Lucchetta et al. [1], based on both the incremental variational principles introduced by Lahellec and Suquet [2] and the formulation proposed by Agoras et al. [3]. However, the Armstrong-Frederick model [4], which is very often used to describe nonlinear kinematic hardening and refers to the framework of non-associated plasticity [5], cannot be handled within the framework of generalized standard materials as required by the incremental variational principles on which the DIV formulation relies. That is why we work with an approximation of this model, namely the modified Chaboche model [6].