Polyethylene oxide (PEO) shows a high CO2-philic due to its dipolar-quadrupolar interaction with CO2 molecules. As a result, it is an excellent candidate for gas separation applications, yet it faces problems such as crystallization and low permeance. Herein, we show a versatile strategy to enhance gas permeation fluxes, which is mainly achieved by hindering the crystallization of PEO and the stacking of nanosheets. Specifically, graphite-like phase carbon nitride (g-C3N4) nanosheets are introduced and interaction networks (PGCN) are constructed by taking full advantage of the dipole-level quadrupole moment interactions between the ether-oxygen groups contained in PEO and CO2. In order to compensate the membrane surface defects for enhancing gas selectivity, we used the suspension coating method to create a PEO@g-C3N4 supported ionic liquid membrane (PGCN/ILX SILM) by coating IL on the surface of membrane. The results show that, when the IL concentration is 30 wt%, the PGCN/IL30% membrane separates CO2/N2 with a CO2 permeance of 1396 GPU and an optimal selectivity of 58. While overcoming the "Trade-off" effect, it has demonstrated good thermal stability and long-term stable operation for 72 h. The development of this work will generate solutions for overcoming PEO crystallization and achieving efficient CO2 capture.