It is not impossible to get approved. In fact, I was recently working with a client who I got qualified with a sub 580 score. If you pay rent on time and don't have any negative hits within the last two years, then you should be good to go. With your combined application, you should easily qualify for the loan needed to buy a $120k home. I have seen people with worse situations still get loans, you just have to talk to the right people and sometimes you have to take a few extra steps.
I work with a mortgage banker who specializes in getting people in your situation qualified for loans. If you are interested, give me a shout via my profile page. If not, good luck with your home purchase! :)
Betina Foreman, Realtor Austin Texas
If you are looking new please give me a call. I can help.
Email me with any questions you may have.
Talk to you soon,
I mostly do "NO PMI" loans which are called conventional home loans. You'll need at least a 620 score to go conventional and at least a 660 to qualify for a No Pmi loan.
Best of luck