We report an investigation of the structural and electronic properties of hybrid superconductor/ferromagnet (S/F) bilayers of composition Nb/Cu₆₀Ni₄₀ prepared by magnetron sputtering. X-ray and neutron reflectometry show that both the overall interfacial roughness and vertical correlations of the roughness of different interfaces are lower for heterostructures deposited on Al₂O₃(1 1 ¯ 02) substrates than for those deposited on Si(111). Mutual inductance experiments were then used to study the influence of the interfacial roughness on the superconducting transition temperature, T_C. These measurements revealed a ∼4% higher T_C in heterostructures deposited on Al₂O₃, compared to those on Si. We attribute this effect to a higher mean-free path of electrons in the S layer, caused by a suppression of diffusive scattering at the interfaces. However, the dependence of the T_C on the thickness of the ferromagnetic layer is not significantly different in the two systems, indicating a weak influence of the interfacial roughness on the transparency for Cooper pairs.