I'm having this issue. A friend of mine transfered his licences so I can download bo3, and its DLC, no problem with that, the game loads up perfectly when I use my profile. However it doesn't let me get online, like if I wasn't connected to Xbox Live. It says that I lost connection and I need to sign in again when using my own account.
And when I use my friend's account it works just fine. We both have gold memberships and we can play any other COD without any problem, it only happens with bo3.
And I checked my NAT Type says open in all games. Hope you can help me.