I don't believe any of the BIAB specific stuff will be found in the Midi file. If you can't figure out the instruments, you can load the Midi file into a sequencer like RealBand or any number of free players out there to see what instruments are in there. Other things like reverb, pan, etc should also be present.

It shouldn't be hard to find the style or very close one in BIAB. Once you enter the feel (Swing, Bossa, etc) and tempo, you can filter the styles to match your settings.

R