Low-mass low-density planets discovered by Kepler in the super-Earth mass regime typically have large radii for their inferred masses, implying the presence of H2-He atmospheres. These planets are vulnerable to atmospheric mass loss due to heating by the parent star's XUV flux. Models coupling atmospheric mass loss with thermal evolution predicted a bimodal distribution of planetary radii, which has gained observational support. However, a key component that has been ignored in previous studies is the dissolution of these gases into the molten core of rock and iron that constitute most of their mass. Such planets have high temperatures (>2000 K) and pressures (∼kbars) at the core-envelope boundary, ensuring a molten surface and a subsurface reservoir of hydrogen that can be 5-10 times larger than the atmosphere. This study bridges this gap by coupling the thermal evolution of the planet and the mass loss of the atmosphere with the thermodynamic equilibrium between the dissolved H2 and the atmospheric H2 (Henry's law). Dissolution in the interior allows a planet to build a larger hydrogen repository during the planet formation stage. We show that the dissolved hydrogen outgasses to buffer atmospheric mass loss. The slow cooling of the planet also leads to outgassing because solubility decreases with decreasing temperature. Dissolution of hydrogen in the interior therefore increases the atmosphere retention ability of super-Earths. The study highlights the importance of including the temperature- and pressure-dependent solubility of gases in magma oceans and coupling outgassing to planetary evolution models.