We present the first direct imaging of a new hydrogel of lipid membranes containing polymer lipids. Freeze-fracture electron microscopy shows unambiguously that the hydrogel's surprisingly large viscoelasticity is explained by a novel defect topology of interconnections between defects. The defects are spherulites with high membrane curvatures which are either isotropic or cylinderlike. A lower concentration of dislocation-type defects was also observed. The interconnections between the defects distinguish the hydrogel from simple “onion” phases of multilamellar vesicles with a smaller viscoelasticity.