Providence-based Providence Equity Partners, a private equity firm that specializes in media company investments, was joined Thursday by Walt Disney Co. as a partner in the popular Hulu Web site founded by NBC Universal and News Corp., the companies said. The deal will put full episodes of Disney’s ABC TV shows, such as Lost, Grey’s Anatomy and Desperate Housewives on Hulu. Disney is the only other media company to join as an equity partner. While other media companies provide content to the Web site, none hold an equity stake. “Hulu is a bright spot in the new media landscape,” said Jonathan M. Nelson, founder and chief executive officer of Providence Equity.