Major challenges in biofabrication revolve around capturing the complex, hierarchical composition of native tissues. However, individual 3D printing techniques have limited capacity to produce composite biomaterials with multi-scale resolution. Volumetric bioprinting recently emerged as a paradigm-shift in biofabrication. This ultra-fast, light-based technique sculpts cell-laden hydrogel bioresins into three-dimensional structures in a layerless fashion, providing unparalleled design freedom over conventional bioprinting. However, it yields prints with low mechanical stability, since soft, cell-friendly hydrogels are used. Herein, for the first time, the possibility to converge volumetric bioprinting with melt electrowriting, which excels at patterning microfibers, is shown for the fabrication of tubular hydrogel-based composites with enhanced mechanical behavior. Despite including non-transparent melt electrowritten scaffolds into the volumetric printing process, high-resolution bioprinted structures were successfully achieved. Tensile, burst and bending mechanical properties of printed tubes were tuned altering the electrowritten mesh design, resulting in complex, multi-material tubular constructs with customizable, anisotropic geometries that better mimic intricate biological tubular structures. As a proof-of-concept, engineered vessel-like structures were obtained by building tri-layered cell-laden vessels, and features (valves, branches, fenestrations) that could be resolved only by synergizing these printing methods. This multi-technology convergence offers a new toolbox for manufacturing hierarchical and mechanically tunable multi-material living structures.