Anyone know about Affordable Housing?

Hi, I am a full time private school teacher in New Jersey and as many of you know, private schools don't pay well. I am 26 and have been teacher for 4 years and make a little under 30,000 a year. I also babysit about 3 days a week for an extra $400-600 a month. My parents are in trouble financially and their home, which I live in is going through forclosure. They have also put me in $14,000 (currently) in credit card debt during my HS and college years. I have always wanted to move out of my home... but never thought it was possible. Now I will have to in a few months anyway or choose to live in a small 2 bedroom apartment with my family of 4. I heard about affordable housing (NJ) through a friend which helps low-income people have the opportunity to buy or rent. I would choose to buy. I tried to make calls to see if I can get an FHA loan pre-approval but so far they said my debt to income ratio it too high. I know I can afford to own under affordable housing because my mom pays the minimum payments on each card and then i pay $400-500 a month from babysitting towards the highest interest card. Half of my monthly salary I save and the other half i pay for my cell bill, car payment, student loans, groceries, gas, ect.. I guess the banks dont see that the income I have and then how much spend and save each month and the fact that my mom pays on my credit cards each month... Does anyone have any advice on how I can afford to purchase a house in NJ under the affordable housing laws?