Recent experiments have created supersolids of dipolar quantum droplets. The resulting crystals lack, however, a genuine cohesive energy and are maintained by the presence of an external confinement, bearing a resemblance to the case of ion Coulomb crystals. We show that a mixture of two antiparallel dipolar condensates allows for the creation of potentially large, self-bound crystals, which, resembling ionic crystals in solid-state physics, are maintained by the mutual dipolar attraction between the components, with no need of transversal confinement. This opens intriguing possibilities, including three-dimensionally self-bound droplet-ring structures, stripe/labyrinthic patterns, and self-bound crystals of droplets surrounded by an interstitial superfluid, resembling the case of superfluid Helium in porous media.