First of all, welcome to HealingWell. I am so happy that you came to us. You will find that the members here are wonderful, and we all understand what you are going through.
Now, take a deep breath and relax. I am sure that this is going to work out for you. Try to take life one day at a time, and I am sure that you will find a job.
To me your bf recording your arguement is a llittle immature on his part. Why would he want to show your mom what was said. Comparing you to her is not a good thing. Everybody is different. And I hope that he isn't making you feel like the bad guy. You may want to rethink this relationship. Though this could be due to his depression, I think that it was a bad thing for him to do.
I know that you want to make this work. So all I can say is go slow with this and see what comes of it. Do you and his mom still get along well? It sounds like you fit in really well with the family.
Try not to read too much into it, but if he continues to act this way, you may want to seperate yourself. You don't deserve to be treated like that and subjecting yourself to this treatment could lower your self esteem.
For the moment take it with a grain of salt, but if it continues, I would have a talk with him. I imagine that the only reason that he did this was to make you look like the bad guy in her eyes, obviously she thinks a lot of you.
I hope that this helped some, keep posting and let us know what is going on.
Remember that you are a wonderful person and don't put up with this if it continues.
Good luck on finding that job. You deserve the best.