The study of surfactant solutions and microemulsions is relevant for many industrial applications that include oil recovery, environmental remediation, and detergency. Understanding the coupled nature of microstructure, phase behavior, and rheology can help in the design of these applications. The microstructure of surfactant solutions and microemulsions determines their equilibrium properties, including phase composition and viscosity. Modeling microemulsion phase behavior by explicitly defining the shape and size of micelles allows for the consistent estimation of phase viscosity. We define a coupled microstructure-phase behavior-viscosity model by considering a two-dimensional lattice, where micelles are assumed to be elliptical. We also define equivalent three-dimensional models, where micelles are assumed to be oblate and prolate spheroids. The compositional dependence of the micellar radii is defined such that the oil-internal-bicontinuous-water-internal structural transitions are consistent with experimental observations. The model offers physical insights by modeling the transition between oil-internal-bicontinuous-water-internal regions in ternary diagrams as critical events, which are then tied to the unusual behavior observed in viscosity and scattering.