Precise and fast determination of position and orientation, which is normally achieved by distance and angle measurements, has broad applications in academia and industry. We propose a dynamic three-degree-of-freedom measurement technique based on dual-comb interferometry and a self-designed grating-corner-cube (GCC) combined sensor. Benefiting from its unique combination of diffraction and reflection characteristics, the absolute distance, pitch, and yaw of the GCC sensor can be determined simultaneously by resolving the phase spectra of the corresponding diffracted beams. We experimentally demonstrate that the method exhibits a ranging precision (Allan deviation) of 13.7 nm and an angular precision of 0.088 arcsec, alongside a 1 ms reaction time. The proposed technique is capable of precise and fast measurement of distances and two-dimensional angles over long stand-off distances. A system with such an overall performance may be potentially applied to space missions, including in tight formation-flying satellites, for spacecraft rendezvous and docking, and for antenna measurement as well as the precise manufacture of components including lithography machines and aircraft-manufacturing devices.