For assembling easy-to-deform and easy-to-broken micropart, accurate acquisition of microassembly force and gripping force during microassembly process while ensuring parallel movement of jaws of microgripper is the key to ensure consistency, accuracy and reliability of microassembly without damage. In addition, simultaneously real-time detection of jaw-displacement of microgripper is also a necessary condition for rapid and accurate microassembly. This paper proposes and realizes a principle of a parallelogram compliant mechanism (PCM) based piezoelectric-actuated microgripper, which simultaneously integrates with microassembly force, gripping force and jaw-displacement sensors for the first time and ensures parallel movement of jaws under no-load and gripping micropart. The major structure of proposed microgripper is a monolithic compliant mechanism (MCM) composed of a primary lever compliant mechanism and three-stage PCM in series. Among them, the third-stage PCM is orthogonal to other two PCM in series. MCM transmits the displacement and force from piezoelectric actuator to jaws while transforming microassembly force, gripping force and jaw-displacement into surface strain of single-notch hinges of PCM with three-stage in series. On this basis, simultaneously sensing microassembly force, gripping force and jaw-displacement is realized by monitoring surface strain of single-notch hinges of three-stage PCM. The sensing equations of the microassembly force, gripping force, and jaw-displacement are established, respectively. A microgripper is manufactured, a microgripper system is realized and the integrated sensors are calibrated. The hysteresis characteristics, creep characteristics and time response are tested experimentally. Two examples of microassembly sub-process are simulated and carried out on the constructed microassembly experimental setup. The theoretical and experimental results show that the designed microgripper can simultaneously acquire the microassembly force, gripping force and jaw-displacement with high sensitivity, linearity and resolution in processes of gripping hohlraum and applying microassembly force to hohlraum while ensuring the parallel movement of the gripping jaws when gripping and not gripping micropart.