Advances in nanoscale self-assembly have enabled the formation of complex nanoscale architectures. However, the development of self-assembly strategies toward bottom-up nanofabrication is impeded by challenges in revealing these structures volumetrically at the single-component level and with elemental sensitivity. Leveraging advances in nano-focused hard x-rays, DNA-programmable nanoparticle assembly, and nanoscale inorganic templating, we demonstrate nondestructive three-dimensional imaging of complexly organized nanoparticles and multimaterial frameworks. In a three-dimensional lattice with a size of 2 micrometers, we determined the positions of about 10,000 individual nanoparticles with 7-nanometer resolution, and identified arrangements of assembly motifs and a resulting multimaterial framework with elemental sensitivity. The real-space reconstruction permits direct three-dimensional imaging of lattices, which reveals their imperfections and interfaces and also clarifies the relationship between lattices and assembly motifs.