Epitaxial Co/Mn/Co trilayers with a wedged Mn layer were grown on Cu(001) and studied by magneto-optical Kerr effect measurements. The bottom Co film as well as the Mn film exhibits a layer-by-layer growth mode, which allows to modify both interface roughnesses on the atomic scale by tuning the thicknesses of the films to achieve a certain filling of their topmost atomic layers. The onset of antiferromagnetic order in the Mn layer at room temperature was found at thicknesses of 4.1 (4.8) and 3.4 (4.0) atomic monolayers (ML) for a filled (half-filled) topmost atomic layer of the bottom Co film in Mn/Co bilayers and Co/Mn/Co trilayers, respectively. Magnetization loops with only one step were found for a trilayer with half-filled topmost atomic layer of the bottom Co film, while loops with two separate steps have been observed in trilayers with an integer number of atomic layers in the bottom Co film. The coercivity of the top Co film shows an oscillation with 1 ML period as a function of the Mn thickness above 10 ML, which is interpreted as the influence of the atomic-scale control of the interface roughness on the interface exchange coupling between the antiferromagnetic Mn and the top ferromagnetic (FM) Co layer. The strength of the magnetic interlayer coupling between the top and bottom Co layers through the Mn layer for an integer number of atomic layers in the bottom Co layer, deduced from minor-loop measurements, exhibits an oscillation with a period of 2 ML Mn thickness, indicative of direct exchange coupling through the antiferromagnetic Mn layer. In addition, a long-period interlayer coupling of the two FM layers with antiparallel coupling maxima at Mn thicknesses of 2.5, 8.2, and 13.7 ML is observed and attributed to indirect exchange coupling of the Rudermann-Kittel- Kasuya-Yosida type.