Covalent organic frameworks (COFs) have been proposed as alternative candidates for molecular sieving membranes due to their chemical stability. However, developing COF membranes with narrowed apertures close to the size of common gas molecules is a crucial task for selective gas separation. Herein, we demonstrate a new type of a two-dimensional layered stacking COF-COF composite membrane in bilayer geometry synthesized on a porous support by successively regulating the growth of imine-based COF-LZU1 and azine-based ACOF-1 layers via a temperature-swing solvothermal approach. The resultant COF-LZU1-ACOF-1 bilayer membrane has much higher separation selectivity for H-2/CO2, H-2/N-2, and H-2/CH4 gas mixtures than the individual COF-LZU1 and ACOF-1 membranes due to the formation of interlaced pore networks, and the overall performance surpasses the Robeson upper bounds. The COF-LZU1-ACOF-1 bilayer membrane also shows high thermal and long-time stabilities.