Two-dimensional (2D) nanosheets (NSs) have shown significant promise as nanofillers in mixed-matrix membranes (MMMs) for overcoming the trade–off between permeability and selectivity. However, the effective regulation of the interlayer spacing of 2D NSs on the separation performance of MMMs remains a challenge. In this study, we adjusted the interlayer spacing of 2D NSs by intercalating layered double hydroxide (LDH) with different anions. The LDH NSs were embedded in a commercial polyether–block–amide (PEBAX 1657) to form MMMs for CO2 separation. The results of our study indicated that increasing the interlayer spacing and intercalated carboxyl groups of the LDH NSs facilitated the fast permeation of CO2 through the membranes. The prepared PEBAX/LDH MMMs (P–LDH series) exhibited promising CO2 permeability, accompanied by good CO2/N2 and CO2/CH4 selectivities. In addition, we demonstrated that methanol enabled the microstructure optimization of the prepared PEBAX/LDH MMMs. The synergistic effects of the intercalated LDH NSs and methanol post–treatment were studied to improve CO2 separation. The prepared MMMs were subjected to scanning electron microscopy (SEM), X-ray diffraction (XRD), FTIR, thermogravimetric analysis (TG), time-lag, positron annihilation lifetime spectroscopy (PALS), and mechanical tests. Methanol-treated MMMs (M–P–LDH series) showed significantly improved CO2 permeability, outstanding CO2/N2 selectivity, and excellent stability for long-term operation under harsh conditions, surpassing Robeson's 2008 upper-bound limit.