Two answers on sources depending on which version of the Realms you're playing:
3.5E FR/pre-Spellplague
FRCS
Lords of Darkness
Champions of Darkness
If you have access, the 2E product The Ruins of Zhentil Keep also has some of the history.
4E FR/post-Spellplague
The campaign setting is the only source.
I actually think this is something your DM should be answering because his version of the Zhentarim may deviate from canon but if you really want more answers about the canon version, I would suggest asking specific questions either here or at the forums on candlekeep.com (unless it's the 4E Zhentarim in which case there is basically no other canon info other than what's in the campaign guide and a few RPGA adventures).
But I do stress specific questions if you want good answers.