The growth of multilayers made from a combination of a weak polyacid and a strongly dissociated polycation is studied as a function of salt concentration and molecular weight. Film thickness reaches a maximum at around 0.3 M salt and then decreases quickly. Preformed multilayers are shown to decompose rapidly and, for high molecular weights, completely when exposed to aqueous solutions of NaCl of concentration >0.6 M. The apparent dissociation of multilayer polyelectrolyte complexes is due to competition for polymer/polymer ion pairs by external salt ions. Similar experiments aimed at decomposing multilayers by protonating the weak acid, thus decreasing polymer/polymer interactions, lead to incomplete loss of polymer, probably due to additional hydrogen bonding from the protonated weak acid. A model based on ion exchange/swelling of multilayers is used to explain their stability and permeability as well as the dependence of film thickness on salt concentration and type.