Vapor deposited multilayers consisting of alternating ferromagnetic and nonferrous metals are being used for magnetic sensing and data storage devices. Their performance is dependent upon interface morphology which is a sensitive function of deposition condition such as the deposition rate, deposition temperature, and flux angle of incidence. A two-dimensional kinetic Monte Carlo method has been developed and used to explore these effects during the growth of model Ni/Cu/Ni multilayers under low adatom impact energy conditions where thermal diffusion is the only mechanism of atomic assembly. An embedded atom method potential with a two-body cross-potential was used for calculation of the activation energies. It takes into account both the atomic configuration of neighboring atoms and their species. Using an extended set of activation barriers the simulations demonstrate that the interface roughness increases almost linearly with increasing layer thickness during the growth, and is more pronounced when depositing a nickel layer than when depositing a copper layer. The deposition of copper is found to help smooth nickel layers. The simulations demonstrate the existence of an optimal growth window in deposition rate–temperature space where the interfacial roughness of a Ni/Cu/Ni multilayer could be minimized. By analyzing the details of individual atomic jumps, the cause of the surface instability is revealed to be the activation and rapid increase of reverse Schwoebel jumps above a temperature threshold.