I don't know any of you, so I can only guess and try to help. Every alter is different, so what might work for one might not work for others. My reading skills with english text suck, so maybe I misunderstood some things. Sorry if I did.
Is it certain that she is crying inside and hating herself? because that would be quite wierd if she doesn't have emotions at all, if all she has is numbness. Jasmine also feels no emotion at all, no hate, no fear, no happyness. The closest thing to an emotion she has is some kind of connection with Jeff. I don't know if it is some kind of feeling or simply her understanding of Jeff meaning no harm at all, but whenever she needs something she first talks to Jeff about it. If he isn't around, she doesn't tell anyone.
I don't know if it can be of any help, but I'll just go and tell how she got that connection with Jeff
Jasmine always loved to be alone, just spend her time by looking at things for hours. No talking, no conversations, only looking at things. She didn't talk because she feels no need to talk to anyone. One day she did want to ask someone to help her moving some things in her home (touching things hurts her), but everytime someone replied it took her a few minutes to understand what has been said, so she just stood there, processing what has been said. The normal reaction for the other was to walk away, since Jasmine didn't do anything anyway, she just stood there like a statue. (which most of us mistook as a sign of nervousness). She also asked Jeff, who just sat down next to her, waiting for her to finish processing everything. Ever since, Jasmine went to Jeff, and she has been talking a bit more too. She might not feel happy or whatever (she feels nothing at all), but she did open up some more. That way we learned more and more about what is going on with her.
Maybe some random informal socializing can help you understand why your alter is depressed? That way you might be able to help her. Just remember that not all alters are as complex as humans, maybe (and I must admit I don't like saying it to you) she just doesn't have happyness, just like Jasmine has no emotions at all.