The middle layer of an artery and vein contains mostly. connective tissue. simple squamous epithelium. smooth muscle. nervous tissue. 2. Arteries carry blood. away from the heart. toward the heart. both away and toward the heart.he middle layer of an artery and vein contains mostly. connective tissue. simple squamous epithelium. smooth muscle. nervous tissue. 2. Arteries carry blood. away from the heart. toward the heart. both away and toward the heart.