This randomized phase II trial studies how well ipilimumab with or without high-dose recombinant interferon alpha-2b works in treating patients with stage III-IV melanoma that cannot be removed by surgery. Monoclonal antibodies, such as ipilimumab, may block tumor growth by targeting certain cells. Recombinant interferon alfa-2b may interfere with the growth of tumor cells. It is not yet known whether ipilimumab is more effective with or without high-dose recombinant interferon alfa-2b in treating melanoma.