CDI files are DiscJuggler images, why would you think that Nero would be able to burn DiscJuggler images? Directly, no, but if you extract the data and audio tracks out of it with tools like
CDmage or
WinISO, you can burn those tracks with the aid of a cue sheet. See instructions for burning ISO+WAV or ISO+MP3 with Nero
here.
Fireburner should work fine; it's pretty
straight forward actually. NTI CD Maker 2000, on the other hand, doesn't have the mixed mode from image feature, or so I've heard, so you can't burn mixed mode from image.