The lipid-protein mixture that covers the lung alveoli, lung surfactant, ensures mechanical robustness and controls gas transport during breathing. Lung surfactant is located at an interface between water-rich tissue and humid, but not fully saturated, air. The resulting humidity difference places the lung surfactant film out of thermodynamic equilibrium, which triggers the buildup of a water gradient. Here, we present a millifluidic method to assemble multilamellar interfacial films from vesicular dispersions of a clinical lung surfactant extract used in replacement therapy. Using small-angle X-ray scattering, infrared, Raman, and optical microscopies, we show that the interfacial film consists of several coexisting lamellar phases displaying a substantial variation in water swelling. This complex phase behavior contrasts to observations made under equilibrium conditions. We demonstrate that this disparity stems from additional lipid and protein gradients originating from differences in their transport properties. Supplementing the extract with cholesterol, to levels similar to the endogenous lung surfactant, dispels this complexity. We observed a homogeneous multilayer structure consisting of a single lamellar phase exhibiting negligible variations in swelling in the water gradient. Our results demonstrate the necessity of considering nonequilibrium thermodynamic conditions to study the structure of lung surfactant multilayer films, which is not accessible in bulk or monolayer studies. Our reconstitution methodology also opens avenues for lung surfactant pharmaceuticals and the understanding of composition, structure, and property relationships at biological air-liquid interfaces.