The development of complex and large 3D vascularized tissue constructs remains the major goal of tissue engineering and regenerative medicine (TERM). To date, several strategies have been proposed to build functional and perfusable vascular networks in 3D tissue-engineered constructs to ensure the long-term cell survival and the functionality of the assembled tissues after implantation. However, none of them have been entirely successful in attaining a fully functional vascular network. Herein, we report an alternative approach to bioengineer 3D vascularized constructs by embedding bioinstructive 3D multilayered microchannels, developed by combining 3D printing with the layer-by-layer (LbL) assembly technology, in photopolymerizable hydrogels. Alginate (ALG) was chosen as the ink to produce customizable 3D sacrificial microstructures owing to its biocompatibility and structural similarity to the extracellular matrices of native tissues. ALG structures were further LbL coated with bioinstructive chitosan and arginine–glycine–aspartic acid-coupled ALG multilayers, embedded in shear-thinning photocrosslinkable xanthan gum hydrogels and exposed to a calcium-chelating solution to form perfusable multilayered microchannels, mimicking the biological barriers, such as the basement membrane, in which the endothelial cells were seeded, denoting an enhanced cell adhesion. The 3D constructs hold great promise for engineering a wide array of large-scale 3D vascularized tissue constructs for modular TERM strategies.