We present a detailed multi‐level investigation of steady‐state three‐phase flow processes in a water‐wet Berea sandstone sample. We use high‐resolution micro‐computed tomography images acquired during micro‐scale core‐flooding experiments which include successive gas injection, waterflooding, and nonspreading oil flooding steps. We develop and employ robust techniques to comprehensively characterize and probe the complex interrelationships between the pore‐scale three‐phase capillary pressures, fluid occupancy, displacement events, and the macroscopic flow behavior. The results demonstrate that the local capillary pressures involving the invading phase rise or drop in compliance with the changes in the macroscopic flow ratios. For instance, the gas‐oil capillary pressures were at their highest levels during the gas injection process (highest gas/oil fractional flow) and dropped during the subsequent processes. More importantly, the oil‐water capillary pressure is found to sharply rise during the gas injection process, implying that the gas‐displacing‐oil‐displacing‐water double displacements are the dominant double displacement mechanism during this experiment. For the waterflooding test, the local gas‐oil capillary pressures consistently decrease due to water‐displacing‐oil‐displacing‐gas double displacement events. Moreover, the results show that the variations in the gas‐liquid capillary pressures are more significant than those in the oil‐water capillary pressures. Also, the variations in all capillary pressures during gas injection are higher than in the subsequent processes. The higher variations in capillary pressure values are attributed to more localized and less uniform pore‐scale events across the medium. Finally, the capillary pressure gradients along the flow direction are incorporated in the three‐phase relative permeability measurements.