We have employed vibrational sum frequency generation (VSFG) to measure for the first time the structure of water at the interface between two bulk immiscible liquids. The OH stretching modes of the interfacial water molecules are examined and compared with analogous studies at the air/water interface. We find that at the oil/water interface the prevailing structure of the water molecules is a tetrahedral arrangement much like the structure of ice, while at the air/water interface we observe an equal distribution between an ice-like and a less ordered water-like arrangement. The relationship between the structure of the interfacial water molecules and the properties of the other fluid (air or oil) is discussed in terms of hydrogen bonding at the interface. We also compare our results to previous VSFG studies and find that our spectrum obtained from the CCl4/water interface differs from what was obtained by others at the hexane/water interface where the hexane is present as a thin layer.