How to buy our first home with low/average credit?

My fiance is trying to get a mortgage loan for our first home because we are expecting our first baby in November. We haven't married yet because I have horrid credit while his is not so bad. However, his score is not high enough to qualify for a loan. It is around 600 and needs to be about 680. He has a personal loan of $4000 that he has been making timely payments on as well as a car payment with the car totaling $14000. He had to get a cosigner for the car. I am unemployed but looking for work; he is a truck driver and makes around $38,000 a year. He tried to get help through a government program but they told us that the funds for that have been exhausted. His parents have their own mortgage and they are willing to help us if possible. What can we do??