By interrogating nature at the length scale of important biological molecules (proteins, DNA), nanotechnology offers great promise to biomedicine. We review here our recent work on nanofilm biomaterials: "nanoscopically" thin, functional, polymer-based films serving as biocompatible interfaces. In one thrust, films containing carbon nanotubes are shown to be highly antimicrobial and, thus, to be promising as biomedical device materials inherently resistive to microbial infection. In another thrust, strategies are developed toward films of independently controllable bioactivity and mechanical rigidity - two key variables governing typical biological responses.