We investigate the impact of high optical depth on the HI saturation observed in the Perseus molecular cloud by using Arecibo HI emission and absorption measurements toward 26 radio continuum sources. The spin temperature and optical depth of individual HI components are derived along each line-of-sight, enabling us to estimate the correction for high optical depth. We examine two different methods for the correction, Gaussian decomposition and isothermal methods, and find that they are consistent (maximum correction factor ~ 1.2) likely due to the relatively low optical depth and insignificant contribution from the diffuse radio continuum emission for Perseus. We apply the correction to the optically thin HI column density on a pixel-by-pixel basis, and find that the total HI mass increases by ~10%. Using the corrected HI column density image and far-infrared data from the IRIS Survey, we then derive the H2 column density on ~0.4 pc scales. For five dark and star-forming sub-regions, the HI surface density is uniform with Sigma_HI ~ 7-9 solar mass/pc2, in agreement with the minimum HI surface density required for shielding H2 against photodissociation. As a result, Sigma_H2/Sigma_HI and Sigma_HI+Sigma_H2 show a tight relation. Our results are consistent with predictions for H2 formation in steady state and chemical equilibrium, and suggest that H2 formation is mainly responsible for the Sigma_HI saturation in Perseus. We also compare the optically thick HI with the observed "CO-dark" gas, and find that the optically thick HI only accounts for ~20% of the "CO-dark" gas in Perseus. ; Comment: accepted for publication in the Astrophysical Journal