AC/DC hybrid microgrids (HMGs) represent a promising architecture that allows the hosting of a mix of ac/dc energy resources and ac/dc loads. Despite their potential, when islanded, HMGs impose operational challenges among of which are precise and stable power sharing, frequency restoration, and voltage regulation. Imprecise power sharing can result in some distributed generators (DGs) being overloaded, while others being underloaded. This article proposes an optimal-power-flow-based optimal power sharing (OPS) scheme to optimize the droop characteristics of DGs and interlinking converters for global power sharing in a multi-DG HMG regardless of DG location and type. The optimized droop parameters might jeopardize the microgrid stability. Thus, the proposed OPS scheme preserves stable power sharing through stability-constrained optimization of the droop characteristics. In addition to DG overloading because of unequal power sharing, voltage-sensitive loads could possibly suffer from voltage deviations because of drooping the voltage with the load increase. The proposed OPS strategy enjoys the ability to regulate the ac/dc voltage within a desired range and restore the nominal frequency. Steady-state and time-domain simulations verify the effectiveness of the proposed sharing scheme in achieving the underlying objectives. Test results also prove the capability of the OPS scheme in zonal power sharing in the case of a distribution grid with multizone ac/dc microgrids.