You need to talk to a local lender who is going to give you an idea of what you can afford based upon income, credit history, down payment. If another adult name will be on the deed, they too will have to go through the same scrutiny. The best think possible is to put yourself and your family in the best financial situation possible when purchasing a home. That may mean leaving the other person off the mortgage and getting something you can afford without the other person's income.
Never rely on someone else to pay our mortgage or other bills unless you are already married. Remember the saying one for all and all for one! You apply as two individuals but the bank counts it as one loan both of you will be responsible for.
Also always consult your financial adviser and attorney on such matters.
If you need further questions answered regarding real estate or otherwise feel free to contact me.