A tissue graft construct for use in repairing diseased or damaged tissues is provided. The tissue graft construct comprises a matrix composition selected from the group consisting of liver basement membrane and extracts and hydrolysates thereof, and processed collagen from vertebrate non-submucosal sources, added endothelial cells, and at least one additional preselected, exogenous population of cells which enhance the initiation of vessel-like structures in the grant. The preselected population of cells can be a population of non-keratinized or keratinized epithelial cells or a population of mesodermally derived cells selected from the group consisting of fibroblasts, smooth muscle cells, skeletal muscle cells, cardiac muscle cells, multi-potential progenitor cells, pericytes, osteogenic cells, and any other suitable cell type, preferably selected based on the tissue to be repaired. Methods for enhancing the vascularization in vivo of these tissue graft constructs and for preparing these graft constructs are also provided.