In this work, a bifunctional model was developed to fit and predict the phase inversion point (PIP) of microemulsions containing polar oils. This model incorporated the hydrophilic-lipophilic difference (HLD) equations, where HLD = 0 at the PIP. The model uses a Langmuir isotherm to account for the interfacial segregation of polar oils as a function of their concentration in the bulk oil phase. The segregated polar oil was treated as being surfactant-like, having a characteristic curvature (Cc). The polar oil in the bulk oil phase was characterized via an equivalent alkane carbon number (EACN). The Cc value was obtained considering deviations in the PIP at low polar oil concentrations. The EACN was determined considering PIP deviations at high polar oil concentrations. Naphthenic acid and dodecanol were used as model polar oils mixed with ionic and nonionic surfactants and nonpolar oils. The EACN of the polar oil was shown to be independent of the EACN of the nonpolar oil and likely independent of the surfactant. The Cc for dodecanol was likely independent of the surfactant used. For naphthenic acid, the Cc was independent of the nonpolar oil, and within a certain surfactant type (ionic, nonionic, or extended ionic), it was likely independent of the surfactant. For the naphthenic acid systems, the segregation predicted via the bifunctional model was consistent with experimental measurements of this segregation. Given that the bifunctional model only involves phase inversion experiments, it is a convenient method to determine the oil-like and surfactant-like nature of polar oils.