In this paper the Helfrich ansatz for bending an amphiphilic monolayer is re-expressed in terms of the deviations in curvature away from a preferred value. Using this expression and a simple model of the response of amphiphiles to interfacial bending, it is demonstrated that there are strict limits to the value of the ratio of the Gaussian curvature modulus to the mean curvature modulus (K-G/K). We have made an estimate of K-G/K from measurements of the swelling behavior in water of inverse bicontinuous cubic mesophases in a system composed of 1-monoolein, dioleoylphosphatidylcholine, and dioleoylphosphatidylethanolamine. The estimate, -0.75 +/- 0.08, is in agreement with the limits set by our model of -1 < K-G/K < 0. This determination is the first to be made on an inverse bicontinuous cubic phase which is sufficiently swollen to be in a regime where first-order curvature elastic energetics should be sufficient to describe the state of the mesophase and hence provide a reliable estimate of K-G/K.