Data Set for the associated article, "Hybrid Biocomposites: From Molecular Behaviour to Material Properties in Silk Fibroin/Cellulose Films". Hybrid biomaterials of silk fibroin and cellulose offer improvements over single-component alternatives in the pursuit of optimised and sustainable materials: showing superior strength, biocompatibility, and flexibility. We investigate the behaviours of fully dissolved and coagulated hybrid films at various compositions and characterise the system with X-ray diffraction, dynamic mechanical thermal, thermogravimetric, and mechanical analyses. We confirm a system optimum in modulus, maximum strength, and maximum strain at failure (2.2 GPa, 28 MPa, and 3.3 % respectively) at 85-95 % cellulose and 5-15 % silk fibroin hybrid composition. Thermogravimetric analysis indicates this is due to increasing interaction density in hybrid compositions correlated with the formation of a hybrid mixed phase up to 4 wt %. We recreate conflicting trends in literature showing sample flexibility improving and reducing with addition of silk fibroin and indicate this is due to variations in sample creep and strain rate. We report a slow stress relaxation and time-dependent viscoelasticity causing this, using comparative mechanical tests at different rates of deformation. We propose a slipping mechanism for stress relaxation similar to those seen in other biopolymer-based biological systems, for example actin filaments in cytoskeletons.