I came to the U.S. as a student, and fell in love with and married a fellow student. He is a U.S. citizen. He submitted all the immigration (adjustment of status) paperwork for me, without a lawyer. I have already been called in for an appointment to take my fingerprints, so I expect to receive the interview appointment notice from USCIS soon.
But now that we are both out of school and working, our relationship does not seem to work so well. In fact, he has moved back in with his mother and father. He is still willing to help me get a green card, if I want it, but is there any point in trying, or will USCIS just think we are committing a fraud and deny my green card and maybe punish us?
It is possible to get a green card when you are living apart and having marital difficulties, so long as you have not gone so far as to get a legal separation (which is possible in some, but not all U.S. states) or actually gotten divorced.
The key thing in deciding whether you deserve a green card (lawful permanent residence) is whether, at the "inception" (beginning) of your marriage, you intended to establish a life together, which it sounds like you did. The USCIS officer is not supposed to judge whether it is a viable, marriage (likely to survive), just whether it is a real marriage as opposed to a fraud. (See I.N.A. Section 204(c).)
Convincing the U.S. Citizenship and Immigration Services (USCIS) officer who interviews you will, of course, be more of a challenge than it would be if the two of you were still living together. In fact, USCIS officers across the various U.S. regions vary in their levels of sophistication and some might, as you fear, take a simpleminded, "marriage ending, deny the green card" approach to your case.
For this reason, hiring an attorney to help with your case could make all the difference. With the law on your side and the right preparation, you stand a good chance of succeeding in your application for permanent residence. Make the most of your husband's willingness to help you, and be sure he accompanies you to the USCIS interview.
The key thing is NOT to lie and pretend that everything is just fine with your marriage. If you get caught in a lie, it can permanently bar you from eligibility for a green card. There's a high likelihood that you would be caught, by the way, perhaps because either you or your husband breaks down and admits the truth after enough questioning. U.S. citizens are notoriously unaccustomed to being interrogated.
So, you will want to explain what happened, and provide accurate information about which of you is living where. Prepare plenty of documentation to bring to your interview to show that your marriage was entered into in good faith and for all the right reasons (legally speaking). (See Documents to Bring to Your Marriage-Based Adjustment of Status Interview for details.)
Also think about what documents you can prepare to show that your marriage has hit the rocks for all the reasons that a real marriage hits the rocks, or that you are bothered by and trying to deal with the situation. Affidavits from friends, counselors, and religious leaders with whom either or both of you has discussed the situation or sought help can be good here. A lawyer can help you prepare these, too (they need to be detailed and convincing).