It is well known that the mechanical behavior of nanoscale multilayered composites is strongly governed by single dislocation mechanisms and dislocation-interface interactions. Such interactions are complex and multiscale in nature. In this work, two such significant effects are modeled within the dislocation dynamics-continuum plasticity framework: elastic properties mismatch (Koehler image forces) and interface shearing in the case of weak interfaces. The superposition principle is used to introduce the stress fields due to both effects solved for by finite elements. The validation of both methodologies is presented. Furthermore, it was found that the layer-confined threading stress of a dislocation in hair-pin configuration increases if the layer is surrounded by layers made of a stiffer material and that this strengthening effect grows more significant as the layer thickness decreases. The observation made through molecular dynamics, that weak interfaces act as dislocation sinks, was also captured with our approach. A dislocation is attracted to the interface independent of its sign or character. Also the force increases sharply as the dislocation approaches the interface. These findings agree with published molecular dynamics simulations and dislocation-based equilibrium models of this type of interaction.