The effect of water thickness on the mean curvature modulus of an inverted bilayer has been investigated. Our system is a lamellar phase made up of a series of water films each surrounded by two ionic surfactant monolayers and separated with hydrophobic solvent. The elastic constant has been estimated using the excess-area method and it is shown to decrease when the thickness of the water layer increases. This result cannot be interpreted in terms of electrostatic effects - an increase of is expected instead - but may arise from a coupling between short-range surfactant interactions and curvature strains.