Delicate interaction control is a crucial issue for automated microsystems dedicated to microobjects handling. This paper proposes a new approach to regulate both position and contact force of a piezoelectric-bimorph microgripper for micromanipulation and microassembly applications. The methodology is developed based on the framework of a discrete-time sliding mode generalized impedance control with adaptive switching gain. One unique feature lies in its easy implementation based on a second-order dynamic model, whereas neither a state observer nor a hysteresis/creep model of the system is required. The stability of the control system is proved in theory, which ensures the tracking performance in the presence of model uncertainties and disturbances. The effectiveness of the scheme is validated by experimental investigations on grasp operation of a microgear. Results show that the approach is capable of accomplishing precision position/force control simultaneously. Moreover, the influences of control gains and target impedance parameters on the tracking performance are addressed, and the achievement of balance between the position and force control accuracy is discussed.