The absorption of infrared radiation within ultra-thin metallic films is technologically relevant for different thermal engineering applications and optoelectronic devices, as well as for fundamental research on sub-nanometer and atomically-thin materials. However, the maximal attainable absorption within an ultra-thin metallic film is intrinsically limited by both its geometry and material properties. Here, we demonstrate that material-based high-impedance surfaces enhance the absorptivity of the films, potentially leading to perfect absorption for optimal resistive layers, and a fourfold enhancement for films at deep nanometer scales. Moreover, material-based high-impedance surfaces do not suffer from spatial dispersion and the geometrical restrictions of their metamaterial counterparts. We provide a proof-of-concept experimental demonstration by using titanium nanofilms on top of a silicon carbide substrate.