Size sieving and Donnan exclusion are generally recognized as the two primary mechanisms governing membrane separation in aqueous systems; however, their respective roles in covalent organic framework (COF) membranes remain insufficiently elucidated. In this work, bilayer COF composite membranes were fabricated by a two-step interfacial polymerization of cationic and anionic COFs. By combining pore-shielding effects with the intrinsic charge of ionic COFs, two types of bilayer membranes were constructed, featuring either smaller effective pore size with weakened surface charge or larger pore size with stronger surface charge. Separation performance was evaluated using dyes and salts with different molecular sizes and charge states. For both membranes, solute rejection decreased with decreasing molecular or ionic size, indicating that size sieving dominates the separation process, whereas Donnan exclusion becomes significant only when solute dimensions approach the membrane pore size. Importantly, in dye/salt mixed solutions, salt-induced surface-charge neutralization markedly reduced dye rejection for the strongly charged COF membrane, while the small-pore, weakly charged COF membrane maintained high dye rejection and salt permeability. The latter membrane exhibited a stable permeance of 115 L·m⁻²·h⁻¹·bar⁻¹ and a dye/salt selectivity of 109 during 300 h of cross-flow filtration. These results demonstrate the dominant role of size sieving and the inherent limitations of Donnan exclusion in COF membrane separations, and suggest that precise pore-size regulation coupled with surface-charge attenuation provides an effective strategy for designing stable, high-performance COF membranes in molecular/ionic separations.