Cardiac tissue engineering is a strategy to replace damaged contractile tissue and model cardiac diseases to discover therapies. Current cardiac and vascular engineering approaches independently create aligned contractile tissue or perfusable vasculature, but a combined vascularized cardiac tissue remains to be achieved. Here, we sought to incorporate a patterned microvasculature into engineered heart tissue, which balances the competing demands from cardiomyocytes to contract the matrix versus the vascular lumens that need structural support. Low-density collagen hydrogels (1.25 mg/mL) permit human embryonic stem cell-derived cardiomyocytes (hESC-CMs) to form a dense contractile tissue but cannot support a patterned microvasculature. Conversely, high collagen concentrations (density ≥6 mg/mL) support a patterned microvasculature, but the hESC-CMs lack cell-cell contact, limiting their electrical communication, structural maturation, and tissue-level contractile function. When cocultured with matrix remodeling stromal cells, however, hESC-CMs structurally mature and form anisotropic constructs in high-density collagen. Remodeling requires the stromal cells to be in proximity with hESC-CMs. In addition, cocultured cardiac constructs in dense collagen generate measurable active contractions (on the order of 0.1 mN/mm(2)) and can be paced up to 2 Hz. Patterned microvascular networks in these high-density cocultured cardiac constructs remain patent through 2 weeks of culture, and hESC-CMs show electrical synchronization. The ability to maintain microstructural control within engineered heart tissue enables generation of more complex features, such as cellular alignment and a vasculature. Successful incorporation of these features paves the way for the use of large scale engineered tissues for myocardial regeneration and cardiac disease modeling.