We investigate the role of top and bottom interfaces in inversion symmetry-breaking Pt/Co/AlOx systems by inserting ultra-thin Cu layers. Wedge-type ultrathin Cu layers (0-0.5 nm) are introduced between Pt/Co or Co/AlOx interfaces. Interface sensitive physical quantities such as the interfacial Dzyaloshinskii-Moriya interaction (iDMI) energy density, the interfacial perpendicular magnetic anisotropy (iPMA), and the magneto-optical Kerr effects (MOKE) are systematically measured as a function of Cu-insertion layer thickness. We find that the Cu-insertion layer in the bottom interface (Pt/Co) plays a more important role in iDMI, PMA, and MOKE. In contrast, the top interface (Co/AlOx) noticeably contributes to only PMA, while its contributions to iDMI and MOKE enhancement are less significant. Although the PMA mainly comes from the bottom interface (Pt/Co), the Cu-insertion layers of all interfaces (Pt/Co, Co/AlOx) influence PMA. For iDMI, only the Cu-insertion layer in the bottom interface exerts SOC suppression which leads iDMI energy to decrease rapidly.