A three-dimensional vector lattice model for a mixture of water, oil and amphiphile is considered on the simple cubic lattice. For a balanced system with equal water and oil concentrations the ground state exhibits, when the surfactant is strong, an ordered bicontinuous structure in addition to pure oil/water and pure surfactant states. The model is transformed, integrating out exactly the surfactant orientational degrees of freedom, in an effective spin-1 model with two-, three, five-and seven-body interactions with temperature dependent interaction strengths. This effective model is then investigated using the local mean-field approximation. The phase diagram of the model is derived and discussed, with particular attention to the structured ordered phase. In the disordered phase a microemulsion region is also found.