Gas permeation characteristics (permeability (P), diffusion (D), and solubility (S) coefficients for CH4, C2H4, C2H6, C3H8, CO2, O2, N2, and Ar and gas separation selectivities) for hybrid materials based on ionic-liquid (IL) saturated MF-4SC membranes in H+ and Ag+ forms and in presence of AgCl nanoparticles have been studied. It has been shown that, in the IL-impregnated MF-4SC membranes in H+ and Ag+ forms, the permeation of CO2 and C2H4 occurs by the facilitated transport mechanism. At the same time, in the presence of AgCl nanoparticles, the facilitated transport mechanism is implemented only for CO2. Diffusion coefficients in the polymer matrix, effective diffusion coefficients between “fixed” carriers, sorption Henry constants in the polymer matrix, and effective interaction constants of CO2 and C2H4 with the membrane material have been determined in terms of the dual-mode sorption model formalism for CO2 and C2H4. It has been shown that the most effective material for the separation of CO2 and C2H4 is an IL-impregnated MF-4SC membrane in a hydrogen form. Using model approaches, it has been shown that the main cause of the facilitated transport of ethylene in these membranes is the interaction between the double bond of the ethylene and the IL cation.