We studied the separation of four practice-relevant gas mixtures on three different membranes which were prepared on porous alumina supports: (i) a pure ZIF-8 (zeolitic imidazolate framework), (ii) a pure PMPS (polymethylphenylsiloxane) polymer, and (iii) a mixed matrix membrane (MMM, with 8.3 wt.% ≈ 8.8 vol.% ZIF-8 (density 0.93 g cm−3) in PMPS (density 1.00 g cm−3)). The four gas mixtures under study were: CO2/CH4, CO2/N2, H2/CO2, and O2/N2. Whereas the pure ZIF-8 membrane shows the best separation factor α = 11 for H2/CH4, the pure PMPS membrane has higher separation factors for the CO2 separation from other gases. It was anticipated that the separation behavior of the MMM results from an interplay of the permeation through the PMPS polymer matrix and the embedded ZIF-8 nanocrystals. Actually, the separation factors of the MMM were found to be equal to the separation factors of the pure polymer membrane. However, we measured much higher gas fluxes through the MMM than through the pure polymer membrane. This experimental finding could indicate an increase of the free volume of the PMPS polymer after introduction of ZIF-8 nanoparticles.