It was shown in a previous paper that the Born-Green-Yvon (BGY) equation in the Fisher-Methfessel approximation is consistent with the AMFA equation of state and results agree quite well with simulation results for bulk phase equilibria and interfacial properties for pure fluids and binary mixtures. Here, the Born-Green-Yvon equation is used to study liquid-liquid and liquid-vapour interfaces in the binary Lennard-Jones mixture methane-perfluoromethane. Firstly, the general phase behaviour is calculated with the AMFA equation of state for two isobars, 0.2 bar and 1 atm. At 1 atm, the phase behaviour is simpler with a liquid-liquid and a liquid-vapour equilibrium region. At 0.2 bar, there is also a liquid-liquid-vapour L1L2V equilibrium. Then the different types of interfaces are calculated for both isobars with the BGY equation. At the lower isobar, perfect wetting is observed in the liquid-vapour interface for bulk liquid phase concentrations close to the liquid-liquid-vapour equilibrium. The BGY results for wetting are discussed and compared with experimental and theoretical investigations in the literature.