Precise measurements of the geometrical thickness of a sample and its refractive index are important for materials science, engineering, and medical diagnosis. Among the possible non-contact evaluation methods, optical interferometric techniques possess the potential of providing superior resolution. However, in the optical frequency region, the ambiguity in the absolute phase-shift makes it difficult to measure these parameters of optically thick dispersive materials with sufficient resolution. Here, we demonstrate that dual frequency-comb spectroscopy can be used to precisely determine the absolute sample-induced phase-shift by analyzing the data smoothness. This method enables simultaneous determination of the geometrical thickness and the refractive index of a planar sample with a precision of five and a half digits. The thickness and the refractive index at 193.414 THz (λ = 1550 nm) of a silicon wafer determined by this method are 0.5204737(19) mm and 3.475625(58), respectively, without any prior knowledge of the refractive index.