The phase behavior of water/n-octane/n-octyl-beta-D-glucopyranoside (C(8)G(1))/1-octanol (C8E0) permits formulating temperature-insensitive microemulsions spanning the whole water-oil composition range. The types of microstructures formed along the trajectory of the middle-phase microemulsion are examined by NMR diffusometry, yielding the respective diffusion coefficients of all the components. The diffusion experiments provide clear evidence of the transition from oil-in-water to water-in-oil microemulsions via bicontinuous structures in a remarkably large range around phase inversion. Small-angle neutron scattering (SANS) along the same path confirm the picture. Furthermore, SANS curves on the absolute scale permit extracting the specific internal interface in the microemulsion as it passes through phase inversion. When the composition of the internal interface is known, the mean area per surfactant molecule is determined. It is found that as the interfacial film becomes increasingly rich in C8E0, that is, the phase inversion is passed, the mean area per surfactant molecule C(8)G(1) decreases along the same progression.