A small-angle neutron scattering (SANS) study is made on a three-component isometric (equal volume fractions of water and oil) ionic microemulsion system, composed of AOT/brine/decane. SANS measurements are made as a function of volume fraction of surfactant within the one-phase channel next to the three-phase region at the hydrophile-lipophile balance (HLB) salinity and at a constant temperature. A previous SANS contrast variation experiment indicated that the microstructure of this type of isometric microemulsion at and around the HLB temperature is bicontinuous in water and oil, with a mono-layer of surfactant film situated at the oil-water interface, having zero mean curvature. We analyze SANS data taken with an oil-water contrast in terms of a modified Berk random wave model. We choose a spectral function which is an inverse 8-th order polynomial in wave number k, containing three length scales l/a, l/b, and l/c. The spectral function has finite second and fourth moments. This threeparameter spectral function is then used in conjunction with Cahn’s clipping scheme to obtain the Debye correlation function for the micro-phase-separated 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 square mean curvature and the average Gaussian curvature of the interface. We determine the variation of these curvatures and the underlying spectral functions as a function of the surfactant volume fraction and discuss their implication on the degree of local order of the bicontinuous structure. We also show 3-d morphologies of two of the microemulsions generated by this model.