Cooperative self-assembly of block copolymers with (in)organic precursors effectively generates ordered nanoporous films, but the porosity is typically limited by the need for a continuous (in)organic phase. Here, a network of homogeneous fibrous nanostructures (≈20 nm diameter cylinders) having high porosity (≈ 60%) is fabricated by cooperative self-assembly of a phenolic resin oligomer (resol) with a novel, nonfrustrated, ABC amphiphilic triblock copolymer template, poly(ethylene oxide)-block-poly(ethyl acrylate)-block-polystyrene (PEO-b-PEA-b-PS), via a thermally induced self-assembly process. Due to the high glass transition temperature (Tg) of the PS segments, the self-assembly behavior is kinetically hindered as a result of competing effects associated with the ordering of the self-assembled system and the cross-linking of resol that suppresses segmental mobility. The balance in these competing processes reproducibly yields a disordered fibril network with a uniform fibril diameter. This nonequilibrium morphology is dependent on the PEO-b-PEA-b-PS to resol ratio with an evolution from a relatively open fibrous structure to an apparent poorly ordered mixed lamellae-cylinder morphology. Pyrolysis of these former films at elevated temperatures yields a highly porous carbon film with the fibril morphology preserved through the carbonization process. These results illustrate a simple method to fabricate thin films and coatings with a well-defined fiber network that could be promising materials for energy and separation applications.