We introduce a novel probe structure for the atomic force microscope. The probe has a sharp tip placed on a micromachined membrane with an integrated displacement sensor, a diffraction-based optical interferometer. We use this probe in a microscope to directly measure the transient interaction forces between the probe tip and the sample when operating in a dynamic mode. We form images related to viscoelasticity and adhesion of the samples by recording salient features of individual tap signals. We also produce tapping mode images of sample topography an order of magnitude faster than current probe microscopes using an integrated electrostatic actuator to move the probe tip. We envision a broad range of applications for this device that range from life sciences to microelectronics.