Using a reactive block polymer precursor, membranes with a bicontinuous nanostructure containing a poly((N,N-dimethylamino)ethyl methacrylate) phase within a cross-linked poly(cyclooctene) framework were formed. These membranes were evaluated for their CO2 selectivity over CH4. Low pressure experiments demonstrated that the CO2 and CH4 permeabilities remain the same with pure and mixed gas feeds. This shows that the membranes are able to maintain their selectivity for CO2. This selectivity was only slightly decreased at moderate temperature (35 °C) and higher pressures (up to 40 bar) using a 50/50 CO2/CH4 mixed gas feed. The bicontinuous block polymer membranes resist the plasticization effect by using a cross-linked phase to sustain the properties of the selective block, and not by changing chain mobility through new chemistry. These bicontinuous block polymer membranes may be valuable for CO2 removal from natural gas streams.