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, namely where 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, we will focus on one of the most crucial ingredients for the understanding of the effective behavious of the composite, namely the quasiconvex hull of the class of deformation gradients. Moreover, we will provide a study of the asymptotic rigidity of the model.