Unemployment benefits, unemployment loan deferment and part time work - Will my deferment be affected? Help?

Just graduated from undergrad last spring. I'm currently unemployed and thus have been able to be under unemployment deferment for my educational loans. I recently accepted a part time position that I start soon - the pay will not exceed the amount I get weekly through unemployment so my understanding is that I'll still be able to claim unemployment weekly and they'll pay me the difference... i.e. if I get $405 weekly through unemployment but my part time job pays me $300, unemployment will pay be $105 or something. I have yet to report this part time job since I haven't started yet. BUT to get to the point, my issue is this: will I still be able to have my loans deferred under unemployment loan deferment even though I have a part time job? I have some loans (including federal) through mygreatlakes and I also have loans through my private alma mater on ecsi.net. I figured if I STILL qualify for unemployment loan deferment, then I should still be able to have this even though I have a part time job that pays me less than my weekly benefit rate. Has anyone been in this situation? I could use some help. I'll probably call my loan providers or something but I wanted to see what you all thought, too. Thanks in advance! :)