We investigate the structural and magnetic properties of interfaces with large lattice mismatch, choosing Pt/Co and Au/Co as prototypes. For our first-principles calculations, we reduce the lattice mismatch to 0.2% by constructing Moiré supercells. Our results show that the roughness and atomic density, and thus the magnetic properties, depend strongly on the substrate and thickness of the Co slab. An increasing thickness leads to the formation of a Co transition layer at the interface, especially for Pt/Co due to strong Pt-Co interaction. A Moiré supercell with a transition layer is found to reproduce the main experimental findings and thus turns out to be the appropriate model for simulating magnetic misfit interfaces.