The atomic force microscope (AFM) has previously been applied to the measurement of surface forces (including adhesion and friction) and to the investigation of material properties, such as hardness. Here we describe the modification of a commercial AFM that enables the stiffness of interaction between surfaces to be measured concurrently with the surface forces. The stiffness is described by the rheological phase difference between the response of the AFM tip to a driving oscillation of the substrate. We present the interaction between silica surfaces bearing adsorbed polymer, however, the principles could be applied to a wide variety of materials including biological samples.