Polymeric materials have drastically changed the society in the last century. However, their non-renewable origin, together with their indiscriminate use and disposal, resulted in a huge accumulation of waste in the environment and raised a wide discussion about the emission of greenhouse gases, which must be considerably reduced to minimize global warming. Thus, the establishment of a consolidated production of polymers prioritizing the use of renewable sources of raw materials became a hot research topic. Vegetable oils are protagonists of this initiative, and their carbon–carbon double bonds are convenient reactive sites for chain growth polymerization reactions. However, typical vegetable oil-based homopolymers often do not display competitive thermo-mechanical properties, and the preparation of the corresponding copolymers and composites is therefore an interesting alternative strategy. Herein, the preparation of composites based on a tung oil/furfuryl alcohol co-continuous network reinforced with bacterial cellulose fibers is described. For this purpose, the cellulose nanofibers were suspended in furfuryl alcohol, and different amounts of the ensuing suspension were mixed with tung oil in the presence of trifluoroacetic acid as cationic initiator. Fourier-transform infrared spectroscopy analysis of all samples indicated the association of both tung oil and furfuryl alcohol in the final materials, with peaks belonging to cellulose superposed at the fingerprint regions of composites. Differential scanning calorimetry and thermogravimetry demonstrated an interesting relationship between the composition and the corresponding thermal properties, and the morphology of the materials was assessed by scanning electron microscopy (SEM), which revealed a homogeneous distribution of cellulosic fibers at lower concentrations. The results gathered here contribute to the development of original macromolecular materials exclusively based on the renewable platform.