We introduce a new technique using small-angle neutron scattering (SANS) to measure the average Gaussian curvature and the average square-mean curvature of the oil-water interface in a threecomponent, nearly isometric (equal volume fractions of water and oil) ionic microemulsion system. The microemulsion is composed of AOT/brine/decane. SANS measurements are made as a function of both the volume fraction of surfactant and salinity at a constant temperature, 45 °C, within the one-phase channel. The temperature is chosen at the hydrophile-lipophile balance (HLB) temperature for a salinity of 0.49%. The SANS data taken with an oil-water contrast are analyzed by using a random-wave model with an appropriate spectral function. The spectral function is an inverse eighth-order polynomial in wave number k, containing three length scales 1/a, 1/b, and 1/c, and has finite second and fourth moments. This three-parameter spectral function is then used in conjunction with Cahn's clipping scheme to obtain the Debye correlation function for the microphase-separated bicontinuous microemulsions. The model shows good agreement with the intensity data in an absolute scale. We then use the three parameters so obtained to calculate the average Gaussian curvature and the average square-mean curvature of the interface. We determine the variation of these curvatures as functions of the surfactant volume fraction and salinity and discuss their implication on the degree of local order of the bicontinuous structure. We also show a 3-D morphology of the microemulsion at the contact point of the three-phase and the one-phase region of the phase diagram generated by this model.