Optical tweezers have emerged as a prominent light-based tool for pico-Newton (pN) force microscopy in mechanobiological studies. However, the efficacy of optical tweezers are limited in applications where concurrent metrology of the nano-sized structures under interrogation is essential to the quantitative analysis of its mechanical properties and various mechanotransduction events. We have developed an all-optical platform delivering pN force resolution in parallel with nano-scale structural imaging of the biological sample by combining optical tweezers with interferometric quantitative phase microscopy. These capabilities allow real-time micromanipulation and label-free measurement of sample's nanostructures and nanomechanical responses, opening avenues to a wide range of new research possibilities and applications in biology.