A model three-component system is considered in which the bonds of a honeycomb lattice are covered by bifunctional molecules of types AA, BB, and AB. The AB type molecule represents an amphiphile. An accurate approximation to the boundary in temperature-composition space of an ordered amphiphile-rich phase is calculated by transforming an accurate closed-form approximation of the critical frontier of an antiferromagnetic phase in an equivalent Ising model. This Ising model has coupling constants and a magnetic field that are temperature dependent.