Coupled lines with a double shielding in weakly and strongly inhomogeneous dielectric media are studied. They have specific properties that allow creation of impedance-transforming directional couplers with given directivity type. The proposed models and synthesis techniques takes into account both electric asymmetry and dielectric inhomogeneity. Numerical simulations and measurements prove the correctness of the general theory, and the possibility of creating co-, contra- and trans-directional couplers with impedance-transforming and phase-shifting properties. The results will be useful for finding new design solutions of advanced couplers and microwave circuits.