We investigate the impact of microscopic roughness on the adhesion and deformation of a rough metal and molecularly smooth mica in contact. Silver and gold films, prepared by thermal evaporation, were brought into contact with mica using the surface forces apparatus; multiple beam interferometry was used to characterize, in situ, both surface deformations and the roughness of the ensuing metal/mica interface. As a basis for comparison, we also present measurements for mica/mica contact. We find that on bringing the metal films into contact with mica, their roughness decreases over time, and concurrently the area of flattened metal/mica contact increases. We measured the adhesion force between mica and metals having different degrees of roughness, and found that adhesive forces are not extinguished until the roughness is greater than about 10 nm. This behavior, as well as the general irreversibility of the adhesion process, indicate that the metal films are undergoing significant plastic deformations.