Cointercalation of graphite with lithium and organic molecules, such as benzene and tetrahydrofuran (THF), is studied using first-principles calculations. The molecules play an important role in expanding the interlayer graphene distance to similar to 7.7 A. The increased space permits multiple H-2 species to be bound to Li cations with a binding energy of 10-22 kJ/mol. Furthermore, in the interstitial area free of Li cations, the negative charge in the graphene sheets enhances the H-2 binding energy to similar to 9 kJ/mol through electrostatic attraction. In order to restrain nucleation of lithium hydrides, the densest Li array is determined to be a Li-4(THF)C-72 structure, which absorbs 3.4 wt % hydrogen molecules reversibly. Cointercalation offers an experimentally accessible approach to designing optimized hydrogen storage materials that have not been investigated previously.