<p>The micromechanical models of the isotropic conductive and elastic polycrystalline solid featuring a general imperfect interface have been developed. In terms of conductivity, the imperfect grain bonding conditions assume a jump of temperature and normal heat flux across the interface. In terms of elasticity, they allow for a jump in displacement and normal traction vectors. The self-consistent homogenization scheme for a polycrystalline solid is formulated in terms of the induced dipole moments and property distribution tensors. The explicit formulas for the effective conductivity and elastic moduli of polycrystalline material are derived from the multipole expansion solution to the model problems under the zero dipole moment condition of the imperfectly bonded inhomogeneity in the effective medium. As a practical application of the developed model, the conductivity and elastic stiffness of the intergranular boundaries of polycrystalline cubic boron nitride are evaluated using the laboratory test data on its macroscopic thermal conductivity and elastic moduli. The interface parameters are found to be strongly dependent on the sintering temperature and hence can serve as an indicator of the consolidation degree of a sintered polycrystalline solid.</p>