It is known that large perpendicular magnetic anisotropy is found at interfaces of cobalt (Co) with palladium (Pd). We investigated Pd/[Co/Pd]30/Pd multilayer thin films with very thin Co and Pd layers with ferromagnetic resonance (FMR) spectroscopy in air and in hydrogen gas. A number of samples characterised by different Pd thicknesses were studied. A ferromagnetic resonance (FMR) peak shift similar to Co/Pd bilayer thin films was observed in the presence of hydrogen gas in the sample environment for all samples. The FMR peak shift is larger for samples with thicker Pd layers. Additionally, we found a dependence of the linewidth on the Pd layer thickness and explain this with the presence of spin pumping.