The interactions between polystyrenesulfonate (PSS)/polyallylamine (PAH) multilayers with human serum albumin (HSA) were investigated by means of scanning angle reflectometry (SAR). We find that albumin adsorbs both on multilayers terminating with PSS (negatively charged) or PAH (positively charged) polyelectrolytes. On films terminating with PSS only, an albumin equivalent monolayer is found whereas when PAH constitutes the outer layer, albumin interacts with the multilayer in such a way as to form a protein film that extends over thicknesses that can be as high as four times the largest dimension of the native albumin molecule. Once the protein film is formed, it is found that when the albumin solution is replaced by a pure buffer solution of same ionic strength as the adsorption solution almost no desorption takes place. On the other hand, when a buffer solution of higher ionic strength is brought in contact with the albumin film, a significant amount of adsorbed proteins is released. One also observes that, for albumin solutions of a given protein concentration, the adsorbed protein amount depends on the ionic strength of the adsorption solution. On surfaces terminating with PAH, the adsorbed protein amount first increases rapidly but passes through a maximum and decreases with the ionic strength. The ionic strength corresponding to the maximum of the adsorbed albumin amount itself depends on the albumin concentration. On the other hand, on films terminating with PSS the adsorbed amount increases with the salt concentration before leveling-off. These results show that the underlying complexity of concentration and pH dependent adsorption/desorption equilibria often simply termed "protein adsorption" is the result of antagonist competing interactions that are mainly of electrostatic origin. We also propose two microscopic models, that are compatible with our experimental observations.