The interaction of deformation twins with interfaces in nanostructured Cu/Ag is studied using molecular dynamics simulations. The influence of the interface structure on twin nucleation, propagation and thickening is analysed, and the role of the misfit interfacial dislocations mesh is detailed. In particular, we show that the interface can induce, directly or indirectly via Lomer dislocations, the nucleation of twinning dislocations. A thorough description of the involved mechanisms is given. Through this atomic scale approach, our study offers some useful understanding of the mechanical twinning process in nanolamellar composites, where twinning appears to be a common plasticity mechanism.