Binary nanoparticle superlattices are periodic nanostructures with lattice constants much shorter than the wavelength of light and could be used to prepare multifunctional metamaterials. Such superlattices are typically made from synthetic nanoparticles, and although biohybrid structures have been developed, incorporating biological building blocks into binary nanoparticle superlattices remains challenging. Protein-based nanocages provide a complex yet monodisperse and geometrically well-defined hollow cage that can be used to encapsulate different materials. Such protein cages have been used to program the self-assembly of encapsulated materials to form free-standing crystals and superlattices at interfaces or in solution. Here, we show that electrostatically patchy protein cages--cowpea chlorotic mottle virus and ferritin cages--can be used to direct the self-assembly of three-dimensional binary superlattices. The negatively charged cages can encapsulate RNA or superparamagnetic iron oxide nanoparticles, and the superlattices are formed through tunable electrostatic interactions with positively charged gold nanoparticles. Gold nanoparticles and viruses form an AB(8)(fcc) crystal structure that is not isostructural with any known atomic or molecular crystal structure and has previously been observed only with large colloidal polymer particles. Gold nanoparticles and empty or nanoparticle-loaded ferritin cages form an interpenetrating simple cubic AB structure (isostructural with CsCl). We also show that these magnetic assemblies provide contrast enhancement in magnetic resonance imaging.