The inhomogeneous texture distribution in a lamellar composite incorporating two dissimilar face-center-cubic metals, i.e., Cu and Ag, under cold rolling is investigated. When the thickness reduction is higher than 80%, the heterogeneity of textures is found in the Cu layer. Namely, in the region adjacent to the rollers the Copper component dominates over the other textures, whereas in the region closed to the heterointerface the Brass component is the dominant texture. Lattice rotations within the heterophase microstructure are then addressed by crystal plasticity finite element modeling that considers not only crystallographic (dislocation slip and twinning) but also non-crystallographic (shear banding) micromechanisms. The simulations show that the hetero-interface between the Cu and Ag layers plays an important role in texture development of the Cu layer when the two metals are co-deformed. In the Cu phase of the studied composite, significant shear banding is triggered by stress concentration at the hetero-interface compared to the positions away from the interface, which leads to the dominant Brass texture in the interface region.