Polymer association at liquid-liquid interfaces is a promising way to spontaneously obtain soft self-healing membranes. In the case of reversible bonding between two polymers, the macromolecules are mobile everywhere within the membrane and they can be absorbed into it at both boundaries due to binding to macromolecules of the other type. In this work, we develop the theoretical model of membrane growth based on these assumptions. The asymptotic dependence of membrane thickness on time as h ~ t^(1/2), as typically observed in experiments in a stationary regime, reveals an interdiffusion-controlled process, where the polymer fluxes sustain the polymer absorption at the membrane boundaries. The membrane growth rate is mainly determined by the difference in equilibrium compositions at the boundaries, the association constant, the polymer lengths and mobilities. This model is further used to describe the growth of hydrogel membranes formed via H-bonding of polymers at the interface between a solution of poly(propylene oxide) (PPO) in isopropyl myristate and an aqueous solution of poly(methacrylic acid) (PMAA). The film thickness is measured by reflectometric methods. The dependence of thickness on time can be approximated by the power law t^(beta), where beta= 1/2 for the PMAA solution at pH=3 and decreases with increasing pH and, hence, ionization degree. The growth rate slows down about 25 times for 500-nm-thick films at pH = 5.1 compared to the case of pH = 3. The ionization degree of PMAA solutions was studied by potentiometric methods. Even a small change in ionization was found to influence the growth rate of the film. A slowdown of the film growth for the ionized polymer can be explained by a drop in the composition gradient in the membrane, as is predicted by the proposed model.< Réduire