Based on the information you provided I think your best option is likely to wait until your credit score improves but you may have a couple of options that enable you to get a mortgage sooner.
The main issue that you face if you and your boyfriend apply for a mortgage together is that your credit score is relatively low and lenders typically use the lower score among co-applicants for a mortgage. Your late payments may also present an issue as lenders usually require that borrowers are current on their debt accounts. Most conventional mortgage programs require a minimum credit score of 680, although certain low down payment programs such as the the HomeReady Program only require a credit score of 620.
The FHA Mortgage Program typically requires a minimum credit score of only 580 although lower scores are permitted under certain circumstances for borrowers who otherwise have strong financial profiles. For example, making a larger down payment and having a steady job history with strong income and relatively low debt are factors that may enable borrowers to qualify for an FHA loan with a low credit score. While I think it is unlikely that you could qualify for an FHA loan today given your credit score, lenders make exceptions on a case-by-case basis so it may be worthwhile to contact lenders to understand what is possible.
You may also want to consider the NACA Mortgage Program. NACA is a not-for-profit organization that offers mortgage programs designed to make homeownership more attainable. For example, the NACA Mortgage Program uses a character-based borrower credit review process instead of using your credit score to qualify for a mortgage. The NACA Program also enables borrowers to purchase a home with no down payment and no closing costs. We provide a detailed overview of the NACA Mortgage Program on FREEandCLEAR and you can contact NACA by visiting the NACA web site.
If you cannot qualify for the programs I outlined above and you and your boyfriend want to apply for a mortgage as co-applicants then your best option may be to wait until your credit score improves before you apply. As you start to make your monthly debt payments on-time and bring your accounts current your credit score should improve over the next several months, although there is no guarantee how long it takes for your credit score to increase. We offer an overview of How to Improve Your Credit Score Before You Apply for a Mortgage that provides some helpful pointers and you can use free on websites like CreditKarma.com, Credit.com or AnnualCreditReport.com to track how your credit score progresses. We also provide a detailed explanation of your credit score and the mortgage process on FREEandCLEAR.
Your other option if you want to buy a home sooner is to have your boyfriend apply for the mortgage as a sole borrower. You could still own the house you buy as joint owners but he alone would be legally responsible for the mortgage. That scenario removes your credit score from the mortgage application process which makes it easier for your boyfriend to qualify for a mortgage. The downside to that scenario is that your monthly income (and debt) is not factored in to determine what size mortgage you can afford. The mortgage you qualify for is solely based on on your boyfriend's financial profile and other borrower qualification factors including his debt-to-income ratio and credit score. Because your income is not factored into the application that means your boyfriend may qualify for a lower mortgage amount on his own than the two of you would qualify for as joint applicants. On the other hand, if you have significant monthly debt payments, your boyfriend may be able to qualify for a larger mortgage amount on his own. You can use our Mortgage Qualification Calculator to determine what size mortgage you can afford based on various monthly gross income and debt expense scenarios.
My ultimate recommendation is that you contact multiple lenders and ask about both the FHA and conventional mortgage programs. You can compare FHA lenders in your area by clicking FHA MORTGAGE RATES We advise you to contact at least four lenders as qualification guidelines vary. Plus, comparing multiple lenders is the best way to save money on your mortgage.