Over the past decades, a population of galaxies invisible in optical/near-infrared (NIR), but bright at longer wavelengths, have been identified through color selections. These so-called optically faint/dark galaxies are considered to be massive quiescent galaxies or highly dust-attenuated galaxies. Having the entire galaxy obscured by dust, however, is likely an extreme case of the much more common occurrence of optically thin and thick absorption coexisting in the same system. With the power of JWST imaging, we are able to spatially resolve massive galaxies at z ∼ 3, accurately model their spectral energy distributions, and identify candidate optically thick substructures. We target galaxies with log ( M * / M ⊙ ) > 10.3 and 2.5 < z < 3.5, and get 486 galaxies in Cosmic Evolution Early Release Science Survey and Public Release Imaging for Extragalactic Research fields. Based on excess NIR luminosity, we identify 162 galaxies (∼33% of the parent sample) as candidate hosts of optically thick substructures. We then carry out spatially resolved spectral energy distribution modeling to explore the physical properties of those dark substructures and estimate the amount of optically thick obscuration. We find that optically thick dust is ubiquitous in normal massive galaxies with a wide variety of star formation rate (SFR) and morphology. 10%-20% of the stellar mass/SFR are unaccounted for in our selected galaxies, and the fraction is insensitive to stellar mass or SFR. The dark substructures are generally dustier than the rest of the galaxies and are irregularly distributed, arguing against an obscured active galactic nucleus as the source of the NIR excess. A correlation between the obscured luminosity and the presence of a recent starburst in the past ≲100 Myr is also observed.