The biochemical activities of microbial communities, or microbiomes, are essential parts of environmental and animal ecosystems. The dynamics, balance, and effects of these communities are strongly influenced by phages present in the population. Being able to characterize bacterium-phage relationships is therefore essential to investigate these ecosystems to the full extent of their complexity. However, this task is currently limited by (i) the ability to characterize complete bacterial and viral genomes from a complex mix of species and (ii) the difficulty to assign phage sequences to their bacterial hosts. We show that both limitations can be circumvented using meta3C, an experimental and computational approach that exploits the physical contacts between DNA molecules to infer their proximity. In a single experiment, dozens of bacterial and phage genomes present in a complex mouse gut microbiota were assembled and scaffolded de novo. The phage genomes were then assigned to their putative bacterial hosts according to the physical contacts between the different DNA molecules, opening new perspectives for a comprehensive picture of the genomic structure of the gut flora. Therefore, this work holds far-reaching implications for human health studies aiming to bridge the virome to the microbiome.