The development of protein-based 3D printable hydrogel systems with tunable structure and properties is a critical challenge in contemporary biomedicine. Particularly, 3D printing of modular hydrogels comprising different types of protein tertiary structure, such as globular and fibrous, has not yet been achieved. Here we report the extrusion-based 3D printing of hybrid hydrogels photochemically co-cross-linked between globular soy protein isolate (SPI) and fibrous silk fibroin (SF) for the first time. The hierarchical structure and organization of pristine SPI and SF, and 1:3 (SPI/SF) hybrid inks under various shear stress were investigated using in situ rheology combined with small-/ultra-small-angle neutron scattering (Rheo-SANS/USANS). The hybrid ink exhibited an isotropic mass fractal structure that was stable between tested shear rates of 0.1 and 100 s-1 (near printing shear). The kinetics of sol-gel transition during the photo-cross-linking reaction and the micromechanical properties of fabricated hydrogels were investigated using photorheology and atomic force microscopy, where the hybrid hydrogels exhibited tunable storage and Young's moduli in the range of 13-29 and 214-811 kPa, respectively. The cross-link density and printing accuracy of hybrid hydrogels and inks were observed to increase with the increase in SF content. The 3D printed hybrid hydrogels exhibited a micropore size larger than that of solution casted hydrogels; where the 3D printed 1:3 (SPI/SF) hybrid hydrogel showed a pore size about 7.6 times higher than that of the casted hydrogel. Moreover, the fabricated hybrid hydrogels exhibit good mouse fibroblast cell attachment, viability, and proliferation, demonstrating their potential for tissue engineering applications.