There are a few red flags here for me:
1- to have that low of a credit score, I assume that he either has a hefty amount of debt, or is having trouble paying on time.
2- with your low income not able to quality for a loan, it makes me wonder how expensive of a house you're looking at, or what you have saved for a down payment.
3- co-signing a loan for an unmarried couple brings up all sorts of legal red flags. this could turn ugly if something goes wrong. I would REALLY suggest against it. If anything happens, the legal action comes down on your parents as they would technically be part owners of the house. Would they really be ok with that?
** Make sure you can even afford what you're attempting to do. It is NOT SMART to stretch yourself beyond your means. For ANY reason. It never ends well, and will set you all up for failure, stressful relationships and hard living situations. **
-how much do you have saved for a down payment? What size/cost of house are you looking at? Can you afford all the monthly 'keep the house running' costs without going over 45% of your monthly income?
-do you have enough money put away in savings (not counting the down payment) to take care of your house costs, family, medical, extra costs for 6months-1year? this is your 'emergency fund' and is EXTREMELY important to have.
- do you have a plan and finances in place in case one of you (especially him) loses a job? baby (or one of you) gets sick and needs emergency care? house needs repair? car dies?
From what you've stated, it sounds like you both don't have the means to purchase a house right now. While sad, it's not a bad situation considering the alternative of purchasing a house, and then potentially losing it and having nothing. I would find a compromise right now with either renting, or perhaps living with family members for awhile until you can save more money for a wedding and a house.
for what its worth -- my now-husband and I both moved back to parents houses after graduating college and had a 2 year engagement. we saved money, and purchased a house right before the wedding. we made sure that ALL house costs could be covered by me, in case he lost his job (he was working for a small start-up.....so he did lose his job after a couple months). Because of our built-up savings and plan in the beginning -- we can continue living comfortably while hubby finds another job.
bottom line - don't dive into something that's going to get you in over your head. you'll be much happier to wait until you can do this more comfortably on your own.