Many natural materials such as intervertebral disk (IVD) are composed of regions with large mismatches in the mechanical properties, yet these regions are integrated through an extremely tough interface. To mimic the mechanical heterogeneity inherent in biological systems, we present here mechanically strong hydrogels consisting of hard and soft components joined together through a strong interface. Stratification of monomer solutions having different densities was used to create two layers of monomer solutions with an interlayer region of a few millimeters in thickness, at which the solutions mix completely. UV-initiated bulk copolymerization of stratified solutions of hydrophilic and hydrophobic monomers leads to the formation of supramolecular, semicrystalline hard/soft hydrogel hybrids with tunable mechanical and thermal properties. By adjusting the comonomer composition in the stratified layers, we were able to create gel/gel interfaces in hybrids that are stronger than their gel components so that they never rupture at the interface region. The hybrids exhibit a high modulus (0.46-74 MPa), tensile strength (0.19-3.9 MPa), and sustain 24-30 MPa stresses at 78-83% compressions, which are comparable to the natural IVD. They also exhibit thermally induced self-healing behavior as well as pseudo triple-shape-memory effect arising from different melting temperatures of crystalline domains belonging to the gel components of hybrids.