Interfaces frequently exist in polycrystalline and multiphase materials. In nanoscale joints, interface properties, such as interface stresses and interface elasticity, influence the stress and displacement field near the interface. Generally, a misfit dislocation exists in the interface due to the mismatch of lattice length in crystals composing the joints. In the present paper, a misfit dislocation is introduced to a coherent interface in order to calculate the stress and displacement distributions in an incoherent interface. A model with an interface zone transferring traction only in the zone from one region to the opposite region is proposed, because these regions slip against each other due to the misfit dislocation. The traction in the interface depends on the displacement and the interface properties. Stresses and displacements considering the interface properties are deduced using a three-dimensional Stroh’s formalism. Bulk stress and displacements around the misfit dislocation are shown to increase with increasing the values of the interface stress and the interface elastic moduli. The stresses and displacements obtained from the derived solutions are compared with those obtained through molecular dynamic (MD) analysis. It is shown that the proposed interface zone model can adequately express the displacement and stress near the misfit dislocation.