In cardiac tissue engineering cells are seeded within porous biomaterial scaffolds to create functional cardiac patches. Here, we report on a bottom-up approach to assemble a modular tissue consisting of multiple layers with distinct structures and functions. Albumin electrospun fiber scaffolds were laser-patterned to create microgrooves for engineering aligned cardiac tissues exhibiting anisotropic electrical signal propagation. Microchannels were patterned within the scaffolds and seeded with endothelial cells to form closed lumens. Moreover, cage-like structures were patterned within the scaffolds and accommodated poly(lactic-co-glycolic acid) (PLGA) microparticulate systems that controlled the release of VEGF, which promotes vascularization, or dexamethasone, an anti-inflammatory agent. The structure, morphology, and function of each layer were characterized, and the tissue layerswere grown separately in their optimal conditions. Before transplantation the tissue and microparticulate layers were integrated by an ECM-based biological glue to form thick 3D cardiac patches. Finally, the patches were transplanted in rats, and their vascularization was assessed. Because of the simple modularity of this approach, we believe that it could be used in the future to assemble other multicellular, thick, 3D, functional tissues.