The interfacial Dzyaloshinskii–Moriya interaction (iDMI) and perpendicular magnetic anisotropy (PMA) can be manipulated via interface engineering. Their strength determines the generation and the size of skyrmions, and the correlation between the iDMI and PMA allows them to be controlled simultaneously, thus choosing the material parameters for which skyrmions can be formed. This opens up the possibility of synthesizing suitable magnetic multilayers that are needed for low-power high-density memory and in logic applications. Vibrating sample magnetometry (VSM), Brillouin light scattering (BLS), and microstrip ferromagnetic resonance (MS-FMR) were used to investigate the correlation between the iDMI and the interface PMA. For this, Pt/Pd(t Pd)Co(t Co)/Au thin film structures with 0 ⩽ t Pd⩽1.2 nm and 1.2 nm ⩽ t Co⩽3 nm were grown by combined sputtering and e-beam evaporation on Si/SiO2 substrates. VSM measurements revealed a negligible magnetic dead layer and a Pd thickness-independent magnetization at saturation of around 1200 emu cm−3. MS-FMR and BLS allowed us to conclue that PMA results from weak volume and interfacial contributions induced by Pd/Co or Pt/Co and Co/Au interfaces. The interface anisotropy constants are found to be 0.65 mJ m−2 and 0.85 mJ m−2 for Pd/Co and for Pt/Co interfaces, respectively. The Pd thickness-dependence of surface iDMI (D s) and PMA (K s) constants follow an exponential decay with a characteristic thickness higher for PMA than the iDMI. The slower decrease of K s vs Pd thickness suggests a shorter range of the iDMI with respect to PMA and points out a strongly localized origin for the iDMI. This difference between the iDMI and PMA is most likely responsible for the nonlinear correlation between PMA and iDMI constants. The investigation of the Co thickness-dependence of the iDMI and PMA in Pd/Co/MgO/Ta systems allows us to conclude a zero iDMI constant of Co/Au and to determine the iDMI constants of Pd/Co and Co/MgO, estimated to be D s Pd/Co = −0.096 pJ m−1 and D s Co/MgO = −0.15 pJ m−1, respectively. The criterion of skyrmions stability, applied for our samples, revealed the possibility of the existence of stable skyrmions in some samples.