We report that polymers can support bilayer membranes to form physical hydrogels of self-healing and tunable isotropic/anisotropic structure. The system consists of poly(dodecyl glyceryl itaconate) (PDGI) which forms lamellar bilayers and polyacrylamide (PAAm) which adsorbs on the bilayer surfaces via hydrogen bond formation. Adsorption of PAAm brings two effects: disturbs the bilayer packing and causes bending of the bilayers; increases the effective thickness of the bilayers and enhances the repulsion between the bilayers due to excluded volume effect. Competition of these two effects brings about sharp superstructure transition from isotropic multilayer foam phase to unidirectionally aligned lamellar phase. Accompanied by this structure transition, the bulk hydrogel exhibits isotropic/anisotropic swelling. The physical gels exhibit high tensile strength and self-healing properties that can be understood by the sacrificial bonds mechanism.