When a low-viscosity wetting fluid displaces a high-viscosity nonwetting fluid along a rough media, an instability may occur: a leading film of invading liquid extends ahead of the advancing fluid-fluid front. Here, we investigate the emergence and evolution of this instability by means of microfluidic experiments and computational modeling. We conduct viscously unfavorable imbibition experiments in a rough Hele-Shaw cell, where one of the surfaces is patterned with cylindrical micropillars. At low flow rate, the displacement is complete with the invading liquid fully saturated across the cell gap. Above a critical flow rate, however, the invading liquid preferentially advances on the rough surface as a leading film, resulting in incomplete displacement. Depending on the flow rate and the degree of roughness, this film may either be confined within the crevices of micropillars as a “thin film” or cover all the surfaces of micropillars as a “thick film”. We propose a phase diagram to delineate these regimes and qualitatively rationalize the transitions. We then develop a phase-field model, which successfully reproduces both the macroscopic patterns and the pore-scale mechanisms, and enables access to quantities (like pressures and fluid saturations) not available experimentally.