A new application for two-dimensional (2D) materials is emulsification, where they can serve as ultrathin platelike interfacial stabilizers in two-liquid systems. We present a first detailed thermodynamic analysis of atomically thin 2D materials at organic-aqueous liquid-liquid interfaces and derive expressions for the transfer free energies of emulsion stabilization that account for material geometry, van der Waals transparency or opacity, and variable hydrophobicity. High mass potency is shown to be an intrinsic property of the 2D geometry, which at the atomically thin limit places every atom in contact with both liquid phases, resulting in unit atom efficiency. The thermodynamic model successfully predicts that graphene oxide but not pristine graphene has a favorable hydrophobic-hydrophilic balance for oil-water emulsion stabilization. Multilayer tiling is predicted to occur by the passivation of droplet surface patches left uncovered by packing inefficiencies in the first monolayer, and complete multilayer coverage is confirmed by cryogenic scanning electron microscopy. The molecular barrier function of graphene interfacial films causes a significant suppression of dispersed-phase evaporation rates with potential applications in controlled release. Finally, these emulsions can be used as templates for creating solid graphene foams or graphene microsacks filled with lipophilic cargos. Emerging 2D materials are promising as dispersants or emulsifiers where high mass potency and multifunctional properties are desired.