Liquid-infused membranes have been introduced to membrane technology recently. The infusion liquid can be expelled, opening the pore, in response to an immiscible feed liquid pressure. In the open state, the pore wall is still covered with the infusion liquid forming the so-called liquid-lined pores. Liquid lining is expected to give anti-fouling properties to these membranes. The pressure-responsive pores can be used for efficient sorting of fluids from a mixture based on interfacial tension. For example, in a two-phase mixture of immiscible liquids, the required liquid entry pressure is different for the constituent liquids. Here, we investigate the capability of liquid-infused membranes for selective permeation of the dispersed phase, that is, oil from an oil-in-water (O/W) emulsion. The separation experiments are conducted in a dead-end pressure-controlled filtration cell using liquid-infused and non-infused membranes. In order to permeate the dispersed phase, oil droplets should come in contact with the membrane surface which is accomplished here by gravity-driven creaming. Our results reveal that by setting the feed pressure between the entry pressure of oil and that of the surfactant solution, oil can be successfully permeated. For high concentrations of surfactants, water also permeated partly. The amount of water permeated through liquid-infused membranes is lower than that through non-infused membranes, caused by the corresponding interfacial tensions. The results suggest that the presence of the infusion liquid in the membrane gives rise to the formation of three-phase interfaces in the pore, namely, the interface between surfactant solution-oil (γ12) and that between oil-infusion liquid (γ23). Based on the interfacial energy contributions, the additional interface between oil and the infusion liquid gives rise to an increase in the liquid entry pressure for the surfactant solution based on the combined interfacial tension (γ12 + γ23) leading to less water permeation.