U.S.-Ukraine Security Cooperation Enhancement Act This bill authorizes the President to treat Ukraine as a major non-NATO ally for purposes of the transfer of defense articles and services until Ukraine accedes to the North Atlantic Treaty Organization (NATO). (Major non-NATO ally status confers various benefits, such as priority for receiving certain excess defense articles.) The bill also expands the Department of Defense's authority to provide security assistance to Ukraine to include the provision of anti-tank, anti-ship, and antiaircraft weapons systems. The Department of State shall report to Congress a review of U.S. security assistance to Ukraine, an assessment of threats to Ukrainian independence, and an assessment of Ukraine's asymmetric capability to counter Russian aggression.