Molecular dynamics simulation is performed to study the stretching characteristics in three Cu/Ta interface models. The crystal structure of Cu layer is changed from single crystal to columnar polycrystal and then to layered twin crystal. The presence of both grain and twin boundaries within Cu layer improves the tensile strength and toughness significantly, demonstrating the fine-grain strengthening. The short-duration plastic deformation in Ta layer starts at the yield point after that the deformation in Cu layer is suppressed, revealing the damage of Cu/Ta interface, and the effect of two kinds of boundaries on the plasticity mainly happens in the early deformation stage. It is interesting that the presence of twin boundary induces the martensitic phase transformation in the early stretching process, while those BCC phases or clusters transform to HCP stacking faults finally. This work will be helpful to understand the role of interface defects in the incipient plasticity of layered metallics, guiding the design of high-performance materials.