Achieving energy-efficient carbon capture with membranes requires materials that combine high gas permeability and selectivity, long-term stability and scalable solution processability. Conventional mixed-matrix membranes (MMMs) cannot fully exploit the intrinsic transport properties of porous filler because high filler loadings often lead to aggregation and non-ideal interfacial effects. Here using a weak-interaction inlaying strategy that overturns the conventional reliance on strong polymer–filler interactions, we report all-organic MMMs that embed single-crystal covalent organic frameworks (COFs) within a continuous polymer matrix. By balancing polymer–filler and filler–filler interaction energies, our approach enables high COF loadings of up to 75.5 vol% while maintaining uniform dispersion and excellent interfacial compatibility. The resulting membranes preserve the intrinsic structure and transport properties of single-crystal COFs, creating filler-dominated pathways for fast CO2 transport. Consequently, they achieve CO2 permeability of 74,800 Barrer while maintaining a CO2/N2 selectivity of ~20. Besides, the MMMs based on polyimide can retain ~85% of the initial permeability after 6 months of ageing at room temperature.