We performed molecular dynamics (MD) simulations to study the effect of interface structure and layer thickness on the mechanical properties of multilayered Cu/Ag composite with Cu{111}//{111}Ag and Cu{100}//{100}Ag interfaces. The results indicate that deformation twinning is the dominant plastic deformation mode in the multilayer with Cu{100}//{100}Ag interfaces and differs from the dislocation slip in the models containing Cu{111}//{111}Ag interfaces. The interfaces in the Cu{111}//{111}Ag multilayer are significantly roughened by dislocation transmission across interfaces. The Shockley partial dislocations are difficult to cross Cu{100}//{100}Ag interface until the interface is twisted by deformation twinning. The deformation twinning in the Ag channel induces twists of Cu{100}//{100}Ag interface, facilitating twinning in Cu channels and dislocation transmitting across the Cu/Ag interface within twin bands. The mechanism results in strong interface roughening. The Cu{110}//{110}Ag interface is formed after the deformation twinning in models containing Cu{100}//{100}Ag interfaces, which exhibits extremely high shear strength than the Cu{100}//{100}Ag interface and produces a weak blocking effect on gliding dislocations.