Multiphase bilayered materials are the constituents of a class of composites made of fine parallel layers of two different kinds. In particular, we work in the single-slip finite crystal plasticity regime, i.e. the materials are made of layers alternatively soft and stiff. In the soft layers a single active slip system with linear self-hardening may occur, while the stiff ones, where the deformation gradient do not have a plastic part, are characterized by two different elastic phases under suitable rank-one connectedness assumptions. After stating the specifics of the model, I will present a study of the asymptotic rigidity of the model.