The mean free path (MFP) within the cobalt (Co) layer is systematically varied over a broad range, from 10 Å to 500 Å, in order to investigate its influence on the current-in-plane magnetoresistance (MR) in ultrathin Co/Cu multilayers. This variation enables a detailed analysis of electron transport mechanisms as a function of spin-dependent scattering within the magnetic layers. The study also examines the effect of surface roughness, which plays a crucial role in electron reflection and scattering at both external and internal boundaries. By incorporating roughness at the outer surfaces and at the Co/Cu interfaces, the model captures realistic structural features often present in experimentally fabricated multilayers. To further isolate the role of interfacial disorder, two distinct interface configurations are considered: a smooth, idealized interface and a rough interface incorporating morphological irregularities. This comparative approach reveals that interface quality significantly modifies the magnetic transport properties of the system. Numerical simulations indicate that MR decreases monotonically with increasing MFP in the case of smooth interfaces, due to reduced spin-dependent scattering. However, for rough interfaces, MR behavior becomes non-monotonic: it may increase or decrease with MFP depending on the dominant spin diffusion and reflection mechanisms at the interface. Overall, the magnitude of MR is found to be highly sensitive to both the degree of surface roughness and the microscopic nature of interfacial scattering, underscoring their fundamental importance in tuning MR effects in magnetic multilayers.