The mechanical properties of metal multilayers change significantly when the modulation period decreases to a nanoscale. As is well known, the lattice misfit between Ni and Cu is~2.7%, it means that the coherent and semi-coherent interfaces can form between the Ni and Cu atomic layer. Hetero-twin interface Cu/Ni multilayer film with a modulation period of several nanometers and grown along the111 direction is realized experimentally, and the mechanical properties change significantly due to the effect of interfaces. In this study, molecular dynamics simulations on Cu/Ni multilayers with coherent, coherent twin, semi-coherent, and semi-coherent twin interfaces under nanoindentation are carried out to study the deformation evolutions of different interfaces and the interactions between dislocation and interfaces. Furthermore, the influence of Cu/Ni interface on the mechanical property is investigated. The simulation results show that the different interface structures exhibit different strengthening and/or softening mechanisms at different indentation depths. The hardness values of the Cu/Ni multilayer films with four different interface structures are different, and the hardness of the coherent interface is larger than the semi-coherent interface's. The hardness values of the four interface structures reside between the pure Cu and pure Ni. For the coherent twin interface, with the increase of the modulation ratio, the strengthening effect of the twin interface is enhanced. The softening effect for the coherent interface is mainly attributed to the generation of parallel dislocations and their proliferation. While for the semi-coherent interface, the mismatched networks are formed at the Cu/Ni interfaces, the softening effect on the movable dislocation is mainly the repulsion of the mismatched network, while the strengthening effect on the movable dislocation is the hindrance of the mismatched dislocation network. The strengthening of the coherent twin interface is attributed to the limited effect of twin interface on the movable dislocation within the monolayer. Unlike the coherent twin interface, the strengthening effect of the semi-coherent twin interface is mainly due to the mutual repulsion between the arched dislocation, which is generated within the twin interface, and the mismatched network. Furthermore, the pinning effect of misfit dislocation network will impede the migration of twin interfaces and will also enhance the mechanical property of Cu/Ni multilayer film.