In this paper, exact stress field solutions are derived for an interfacial disclination dipole in an hcp bicrystal with an imperfect interface described by the traction discontinuity, displacement discontinuity and slipping models. The solutions show that the stress variation is not necessarily monotonic with worsening imperfection and can exceed 100% of the stresses in bicrystals with perfect interfaces. A strong bias exists between the influence of the normal and shear traction jump parameters, and between the influence of the normal and tangential displacement jump parameters, on the interfacial stresses. The traction and displacement discontinuity models also predict very different dependence of the interfacial stresses on the jump parameters. These results suggest that imperfect interfaces may significantly raise the internal stresses and thus drastically alter the damage mechanisms (nucleation and propagation of dislocations/cracks, fatigue, etc.) as well as the mechanical properties (effective properties, failure modes, strength, etc.) of polycrystalline materials.