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New configuration of anisotropic 3-D composite right/left-handed (CLRH) metamaterial structures is proposed and designed. It is composed of stacked layers using conductive mesh plates and dielectric layers including 2-D array of dielectric resonators. Balanced CLRH transmission structures are designed not only for both polarization and propagation directions in the layer plane, but also for the normal propagation. The structure is essentially anisotropic and has significant polarization dependence for the wave propagation. Still, for the wave propagation with the polarization parallel to the mesh plates, it can provide relatively small anisotropic propagation characteristics in a certain frequency region if the configuration parameters are appropriately designed. Additionally, it is numerically confirmed that the designed structure shows the left-handedness for the in-plane propagation with the normal polarization, but not right-handedness. The negative-refractive-index flat lens is experimentally demonstrated for validation.