The protection of the viral genome during extracellular transport is an absolute requirement for virus survival and replication. In addition to the almost universal proteinaceous capsids, certain viruses add a membrane layer that encloses their double-stranded (ds) DNA genome within the protein shell. Using the membrane-containing enterobacterial virus PRD1 as a prototype, and a combination of nanoindentation assays by atomic force microscopy and finite element modelling, we show that PRD1 provides a greater stability against mechanical stress than that achieved by the majority of dsDNA icosahedral viruses that lack a membrane. We propose that the combination of a stiff and brittle proteinaceous shell coupled with a soft and compliant membrane vesicle yields a tough composite nanomaterial well-suited to protect the viral DNA during extracellular transport.