The addition of saturated fatty acids (FA) to phosphatidylcholine lipids (PC) that have saturated acyl chains has been shown to promote the formation of lyotropic liquid-crystalline phases with negative mean curvature. PC/FA mixtures may exhibit inverse bicontinuous cubic phases (Im3m, Pn3m) or inverse topology hexagonal phases (HII), depending on the length of the acyl chains/fatty acid. Here we report a detailed study of the phase behavior of binary mixtures of dioleoylphosphatidylcholine (DOPC)/oleic acid (OA) and dioleoylphosphatidylethanolamine (DOPE)/oleic acid at limiting hydration, constructed using small-angle X-ray diffraction (SAXD) data. The phase diagrams of both systems show a succession of phases with increasing negative mean curvature with increasing OA content. At high OA concentrations, we have observed the occurrence of an inverse micellar Fd3m phase in both systems. Hitherto, this phase had not been reported for phosphatidylethanolamine/fatty acid mixtures, and as such it highlights an additional route through which fatty acids may increase the propensity of bilayer lipid membranes to curve. We also propose a method that uses the temperature dependence of the lattice parameters of the HII phases to estimate the spontaneous radii of curvature (R0) of the binary mixtures and of the component lipids. Using this method, we calculated the R0 values of the complexes comprising one phospholipid molecule and two fatty acid molecules, which have been postulated to drive the formation of inverse phases in PL/FA mixtures. These are -1.8 nm (±0.4 nm) for DOPC(OA)2 and -1.1 nm (±0.1 nm) for DOPE(OA)2. R0 values estimated in this way allow the quantification of the contribution that different lipid species make to membrane curvature elastic properties and hence of their effect on the function of membrane-bound proteins.