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Abstract Erosional perturbations from changes in climate or tectonics are recorded in the profiles of bedrock rivers, but these signals can be challenging to unravel in settings with non‐uniform lithology. In layered rocks, the surface lithology at a given location varies through time as erosion exposes different layers of rock. Recent modeling studies have used the Stream Power Model (SPM) to highlight complex variations in erosion rates that arise in bedrock rivers incising through layered rocks. However, these studies do not capture the effects of coarse sediment cover on channel evolution. We use the “Stream Power with Alluvium Conservation and Entrainment” (SPACE) model to explore how sediment cover influences landscape evolution and modulates the topographic expression of erodibility contrasts in horizontally layered rocks. We simulate river evolution through alternating layers of hard and soft rock over million‐year timescales with a constant and uniform uplift rate. Compared to the SPM, model runs with sediment cover have systematically higher channel steepness values in soft rock layers and lower channel steepness values in hard rock layers. As more sediment accumulates, the contrast in steepness between the two rock types decreases. Effective bedrock erodibilities back‐calculated assuming the SPM are strongly influenced by sediment cover. We also find that sediment cover can significantly increase total relief and timescales of adjustment toward landscape‐averaged steady‐state topography and erosion rates.