We study interfacial fluctuations in a Ginzburg-Landau model for ternary oil-water-surfactant mixtures by Monte Carlo simulations. Space has to be discretized in order to apply the Monte Carlo method. However, by an appropriate choice of the lattice constant of the background lattice, discretization effects can be largely avoided. Strong fluctuation effects on the phase diagram are observed, which can be explained by a fluctuation-induced lowering of the oil-water interfacial tension. We determine several quantities, which characterize the structure of the microemulsion, such as the internal interfacial area and the Euler characteristic. The microemulsion phase is shown to have a disordered bicontinuous structure. In the lamellar phase, we observe an increase of the interfacial area with increasing separation of the monolayers. A quantitative comparison with the predictions of the effective curvature model of Helfrich [J. Phys. (Paris) 46, 1263 (1985)] yields excellent agreement, when an exponential distance dependence of the interfacial tension is taken into account.