Regions on a host protein that interact with virus proteins (exogenous interfaces) frequently overlap with those that interact with other host proteins (endogenous interfaces), resulting in competition between hosts and viruses for these shared interfaces (mimic-targeted interfaces). Yet, the evolutionary consequences of this competitive relationship on the host are not well understood. Here, we integrate experimentally determined structures and homology-based templates of protein complexes with protein-protein interaction networks to construct a high-resolution human-virus structural interaction network. We perform site-specific evolutionary rate analyses on this structural interaction network and find that exogenous-specific interfaces evolve faster than endogenous-specific interfaces. Mimic-targeted interfaces evolve as fast as exogenous-specific interfaces, despite being targeted by both human and virus proteins. Our findings suggest that virus targeting plays a dominant role in host interfacial evolution within the context of domain-domain interactions and that mimic-targeted interfaces on human proteins are the key battleground for a mammalian-specific host-virus evolutionary arms race.