Preparation methods are presented of thin dual layer membranes (DLM's) and mixed matrix membranes (MMM's) based on nanosheets of the Cu-BDC metal-organic framework (MOF, lateral size range 1–5 µm, thickness 15 nm) and commercially available poly(ethylene oxide)–poly(butylene terephthalate) (PEO–PBT) copolymer (Polyactive™) and their performances are compared in CO₂/N₂ separation. The MMMs and DLMs represent two extremes, on the one hand with well-mixed components and on the other hand completely segregated layers. Compared to the free-standing membranes, the thin PAN- and zirconia-alumina-supported MMMs showed significant enhancement in both permeance and selectivity. The support properties affect the obtained selective layer thickness and its resistance impacts the CO₂/N₂ selectivity. The permeance of thin DLM's is among the highest reported literature data of MOF based thin MMMs, but have a modest selectivity. Addition of the nanosheets in the thin MMMs improves the CO₂/N₂ selectivity of the already selective polymer further to 77. The nanosheets in the thin MMMs make a gutter layer on the PAN support superfluous. The small pore support ZrO₂-alumina does not need a gutter layer. XRD analysis reveals that the spatial distribution of MOF nanosheets and polymer chains packing were responsible for differences in the permeation performance of the free-standing, thin dual layer and mixed matrix membranes.