The introduction of molecularly woven three-dimensional (3D) covalent organic framework (COF) crystals into polymers of varying types invokes different forms of contact between filler and polymer. Whereas the combination of woven COFs with amorphous and brittle polymethyl methacrylate results in surface interactions, the use of the liquid-crystalline polymer polyimide induces the formation of polymer-COF junctions. These junctions are generated by the threading of polymer chains through the pores of the nanocrystals, thus allowing for spatial arrangement of polymer strands. This offers a programmable pathway for unthreading polymer strands under stress and leads to the in situ formation of high-aspect-ratio nanofibrils, which dissipate energy during the fracture. Polymer-COF junctions also strengthen the filler-matrix interfaces and lower the percolation thresholds of the composites, enhancing strength, ductility, and toughness of the composites by adding small amounts (~1 weight %) of woven COF nanocrystals. The ability of the polymer strands to closely interact with the woven framework is highlighted as the main parameter to forming these junctions, thus affecting polymer chain penetration and conformation.