Nowadays, the imidazolium-based ionic liquids containing acetate counter-ions are attracting much attention as both highly selective absorbents of the acidic gases and CO₂ carriers in the supported ionic liquid membranes. In this regard, the investigation of the gas transport properties of such membranes may be appropriate for better understanding of various factors affecting the separation performance and the selection of the optimal operating conditions. In this work, we have tested CH₄, CO₂ and H₂S permeability across the SILM impregnated by 1-butyl-3-methylimidazolium acetate (bmim[ace]) with the following determination of the ideal selectivity in order to compare the facilitated transport membrane performance with the SILM that dissolves acidic gases physically, namely, containing 1-butyl-3-methylimidazolium tetrafluoroborate (bmim[BF₄]). Both SILMs have showed modest individual gases permeability and ideal selectivity of CO₂/CH₄ and H₂S/CH₄ separation that achieves values up to 15 and 32, respectively. The effect of the feed gas mixture composition on the permeability of acidic gases and permeselectivity of the gas pair was investigated. It turned out that the permeation behavior for the bmim[ace]-based SILM toward the binary CO₂/CH₄, H₂S/CH₄ and ternary CO₂/H₂S/CH₄ mixtures was featured with high acidic gases selectivity due to the relatively low methane penetration through the liquid phase saturated by acidic gases.