A lattice gas of trigonal-planar cations and anions on the triangular lattice is constructed to model the adsorption of guanidinium nitrate at the mercury-water interface. For physically realistic intermolecular interactions and electrochemical potentials, the Pirogov-Sinai theory is used to rigorously prove the presence at low temperatures of a hexagonal hydrogen-bonded phase in the model. This phase is consistent with the monolayer structure recently proposed on the basis of experiments.