We investigate theoretically the interfacial properties of supercooled water, both with respect to the vapor-liquid and, for the first time, for the hypothesized low-temperature liquid-liquid transition. We use the van der Waals theory of interfaces, together with two closely related microscopic models of waterlike associating fluids. We find that the predicted interfacial tension associated with the vapor-liquid transition is 2 orders of magnitude larger than the corresponding liquid-liquid transition, and we explain this result largely in terms of the very different ranges of densities spanned by each transition. Anomalous behavior in the temperature dependence of the vapor-liquid interfacial tension is predicted in all cases. We obtain good agreement with experimental values for the thickness and tension of the vapor-liquid interface.