The formation of diamond structures from tailorable building blocks is an important goal in colloidal crystallization because the non-compact diamond lattice is an essential component of photonic crystals for the visible-light range. However, designing nanoparticle systems that self-assemble into non-compact structures has proved difficult. Although several methods have been proposed, single-component nanoparticle assembly of a diamond structure has not been reported. Binary systems, in which at least one component is arranged in a diamond lattice, provide alternatives, but control of interparticle interactions is critical to this approach. DNA has been used for this purpose in a number of systems. Here we show the creation of a non-compact lattice by DNA-programmed crystallization using surface-modified Qβ phage capsid particles and gold nanoparticles, engineered to have similar effective radii. When combined with the proper connecting oligonucleotides, these components form NaTl-type colloidal crystalline structures containing interpenetrating organic and inorganic diamond lattices, as determined by small-angle X-ray scattering. DNA control of assembly is therefore shown to be compatible with particles possessing very different properties, as long as they are amenable to surface modification.