LAN/XBOX Live multiplayer mode conflict?

Looks like LAN and XBOX Live multiplayer modes are interfering with each other. When both switches are on, sometimes the game displays as an XBOX game, and sometimes as a LAN game. It is impossible to connect to XBOX - "Unable to connect to world". When only the LAN switch is on, everything works perfectly. When only XBOX switch is on, I still can't connect to the XBOX game.