If the DLC doesn't show up in Aurora or Freestyle Dash, go to Settings > Content Settings > Manage Game Paths and ensure your depth is set high enough (usually 3 or 4) to find the deep subfolders.
Getting DLC to work on a for the Call of Duty: Black Ops series requires specific folder structures and, often, a few extra steps to "unlock" the content so the console recognizes it as licensed. 1. Basic DLC Installation Path Call of Duty Black Ops [Jtag/RGH DLC]
If XM360 fails, you can use this PC-based tool to unlock the files before transferring them to your Xbox. 3. Essential: Title Updates (TU) If the DLC doesn't show up in Aurora