We present a novel approach for studying membrane formation by the interaction of polymers and surfactants with opposite charge using a Hele-Shaw experimental setup. A solution of the anionic biopolymer xanthan gum is placed in direct contact with a CnTAB surfactant solution (n = 10, 12, 14, and 16). Thereby, a polymer-surfactant membrane spontaneously forms between the two solutions due to the precipitation of polymer-surfactant complexes, which grows afterwards in the direction of the polymer solution. The dynamics of the growth of the membrane thickness and the mass transfer of polymer are evaluated for different surfactant types and concentrations. The experiments and supporting numerical calculations indicate that polymer mass transfer is driven by diffusion of the charged macromolecules along the concentration gradient, which is coupled to the electric field induced by the faster diffusion of the more mobile counterions. The properties and structure of the formed membrane significantly depend on the surfactant hydrophobicity and concentration. In addition, in a wide range of experiments, the formation of a porous structure in the membrane is observed whose characteristics can be tuned by the process parameters. A mechanism is proposed for the pore formation explaining it as an instability of the growing membrane surface in interaction with the supply of polymer across the depleted zone in the vicinity of the membrane front.