We investigate the correlation between roughness, remanence and coercivity in Co/Ni films grown on Cu seed layers of varying thickness. Increasing the Cu seed layer thickness of Ta/Cu/8x[Co/Ni] thin films increases the roughness of the films. In-plane magnetization loops show that both the remanance and coercivity increase with increasing seed layer roughness. Polar Kerr microscopy and magnetic force microscopy reveal that the domain density also increases with roughness. Finite element micromagnetic simulations performed on structures with periodically modulated surfaces provide further insight. They confirm the connection between domain density and roughness, and identify the microsocpic structure of the domain walls as the source of the increased remanence in rough films. The simulations predict that the character of the domain walls changes from Bloch-like in smooth films to Neel-like for rougher films.