You technically are out of luck because your name is not on the mortgage and or title. Your recent business history shouldn't prevent you from getting the mortgage in both your names. You have a past history, that they will ask for. If you are getting a Fanne Mae mortgage (for 1st time homebuyer's), your past tax returns willl be enough.
This is how I would handle this, personally.
You would have to have an agreement with your friend that each of you would split the deductions. I would do this legally. This is an iffy situation. If your friend decides to take the full deduction, the IRS will disallow yours and penalties and interest can accrue.
Personally, I would not do this. Legally, you have nothing. If you are putting money into the down payment, you could stand to lose it. If anything happens to your friend, you could lose everything. Because you are "friends" you are not legally entitled to anything, even if the house is left to you in a will. That will could be very easily contested by a famil;y member. If your name is not on the mortgage/title, I wouldn't do it.