The interaction between interface dislocation networks and a single lattice Volterra-type dislocation is analyzed by superposition using anisotropic elastic theory in dissimilar materials. The general and nontrivial field solutions for the displacements and stresses are derived by applying the Stroh sextic formalism and Fourier transform in heterogeneous bimaterials. The present approach therefore enables the calculation of the elastic interaction forces for the glide and climb components with different elastic constants and unequal partitioning of elastic fields between adjacent crystals neighboring a semicoherent heterophase interface. Two-dimensional application examples to the pure misfit Au/Cu interface are evaluated, where the infinitely long straight lattice dislocation, parallel to the interface dislocations, is embedded in Au. The repulsive and attractive interaction forces between these two types of (intrinsic and extrinsic) defects are investigated and discussed, for which the results provide a novel basis for examining multiple large-scale dislocation interactions in anisotropic interface-dominated materials with accurate mechanical boundary conditions.