The use of an azine-linked covalent organic framework (ACOF-1) as filler in mixed-matrix membranes (MMMs) has been studied for the separation of CO2 from N-2. To better understand the mechanisms that govern separation in complex composites, MMMs were prepared with different loadings of ACOF-1 and three different polymers as continuous phase: low flux-mid selectivity Matrimid (R), mid flux-high selectivity Polyactive (TM) and high flux-low selectivity 6FDA: DAM. The homogeneous distribution of ACOF-1 together with the good adhesion between the ACOF-1 particles and the polymer matrices were confirmed by scanning electron microscopy. In mixed-gas CO2/N-2 separation a clear influence of the polymer used was observed on the performance of the composite membranes. While for Matrimid (R) and 6FDA: DAM an overall enhancement of the polymer's separation properties could be achieved, in case of Polyactive (TM) penetration of the more flexible polymer into the COF porosity resulted in a decreased membrane permeability. The best improvement was obtained for Matrimid (R)-based MMMs, for which a selectivity increase from 29 to 35, together with an enhancement in permeability from 9.5 to 17.7 Barrer for 16 wt% COF loading, was observed. Our results demonstrate that the combination of the filler-polymeric matrix pair chosen is crucial. For a given filler the polymer performance improvement strongly depends on the polymeric matrix selected, where a good match between the discontinuous and continuous phase, both in the terms of compatibility and gas separation properties, is necessary to optimize membrane performance.