The Widom model of microemulsions is defined by a spin-1/2 Ising simple cubic lattice with ferromagnetic nearest neighbor interactions, antiferromagnetic next-nearest neighbor interactions and half as strong antiferromagnetic interactions at distance = 2. We compare the mean-field predictions of the Widom group with our Monte Carlo simulations of the phase diagram and interfaces. One of the predicted phases is shown to be unstable, and in another the transition temperature differs by a factor 3. Other mean field predictions are in good agreement with our simulations. For the interface with amphiphilic molecules in between oil and water large widths are observed for higher temperatures, and the interface energy vanishes at the stability limit of the ferromagnetic phase at low temperatures, as is required for an appropriate description of microemulsions. Large clusters are found if the numbers of molecules, instead of their chemical potentials, are kept constant in the simulation. We also check Shnidman's predictions for a different model of binary micellar solutions and find that this model also leads to complex phases.