We investigate the multicast of layered multimedia content in single hop cognitive radio (CR) networks and ways of improving the subscriber utility. The proposed unified opportunistic scheduling (UOS) aggressively utilizes diversity potential present in CR by exploiting two types of multiuser diversity (MUD), one between multicast groups and another between data stream subscribers in a group. As a result, the resource usage efficiency is significantly increased, and better utility can be achieved. According to derived effective average subscriber throughput under unified MUD, a scheduling algorithm is designed to approach the theoretical throughput improvement. We specifically introduce controlled competition between multicast groups to balance the increasing resource efficiency and the risk of overstretching the limited available spectrum. The algorithm combines prioritization, rateless coding, and data fragmentation to inherently cope with dynamic spectrum availability in CR. The presented simulation results show improved performance in various situations in comparison to other schemes not taking full advantage of the present MUD potential.