The distance-dependent interaction between multilayers of alternating polycation (poly-L-lysine) and polyanion (poly-L-glutamic acid) deposited onto mica surfaces in aqueous solution is investigated with the surface force apparatus. At large separations, a long-range, weak attraction is observed. The interaction turns into repulsion as opposite multilayers overlap when the surface separation is reduced. The initially observed exponential force-distance law is ultimately overcome by a steep steric interaction at full compression of the films. The evolution of the force profiles as a function of time and upon subsequent unload-load sequences is monitored. The origin of the different interaction regimes arises from osmotic pressure and the formation of complexes between the oppositely charged chains.