Cardiac tissue engineering strategies have the potential to regenerate functional myocardium following myocardial infarction. In this study, we utilized novel electrospun fibrin microfiber sheets of different stiffnesses (50.0 ± 11.2 kPa and 90.0 ± 16.4 kPa) to engineer biomimetic models of vascularized cardiac tissues. We characterized tissue assembly, electrophysiology, and contractility of neonatal rat ventricular cardiomyocytes (NRVCMs) cultured on these sheets. NRVCMs cultured on the softer substrates displayed higher conduction velocities (CVs) and improved electrophysiological properties. Human umbilical vein endothelial cells (HUVECs) formed dense networks on the sheets when co-cultured with human adipose-derived stem/stromal cells (hASCs). To achieve vascularized cardiac tissues, we tested various tri-culture protocols of NRVCM:hASC:HUVEC and found that a ratio of 1,500,000:37,500:150,000 cells/cm2 enabled the formation of robust endothelial networks while retaining statistically identical electrophysiological characteristics to NRVCM-only cultures. Tri-cultures at this ratio on 90 kPa substrates exhibited average CVs of 14 ± 0.6 cm/s, Action Potential Duration (APD)80 and APD30 of 152 ± 11 ms and 71 ± 6 ms, respectively, and maximum capture rate (MCR) of 3.9 ± 0.7 Hz. These data indicate the significant potential of generating densely packed endothelial networks together with electrically integrated cardiac cells in vitro as a physiologic 3D cardiac model.