Great question....actually great questionS!
Traditional underwriting guidelines allow for a rental credit of 75% to offset the mortgage, taxes and insurance of any rental property. For example, rent of $1000 would give you "income" of $750. If the total mortgage was $1000, underwriting would calculate a debt of $250. The lender may require an appraisal of the property to determine "fair market rent" (this is a lender specific issue, some would just require a lease agreement). Note: the use of a 25% vacancy factor for rental property is an industry standard. The suggestion below that lenders will use 80-90% is completely erroneous information.
Again, the above is an explanation of traditional underwriting guidelines; however, there are very little standards that are industry wide in today's market. Most lenders are now requiring a two year history of rental income (on tax returns) before allowing any use of rental income. However, some lenders may waive that requirement if you have 25% or more equity in the property (as you stated). Again, an appraisal may be required. My company would not allow me to use any rental income; however, I have seen comments from mortgage professionals that indicate they can still use the rental income.
I have not heard the 3 times income rule in a long time and find it more out dated and misleading than ever before. It MAY be useful for a consumer to try to determine what he/she would be comfortable with; however, the calculation would have no relevance to mortgage qualifications to assist with getting your financing approved.
Several issues in your comment would be addressed and questioned in the underwriting process:
1). Moving to Maryland? Transferring with your job? New job/company? Underwriting is going to be very focused on the stability of your income.
2). Separating and dividing the mortgage payment (off set by rents received). Underwriting is going to address this issue very conservatively. In fact, I would expect more lenders to "hit" your debt to income with the entire mortgage payment with no credit for rent. If you and your co-owner had a history of six or twelve months, I could see the underwriter being more lenient; however, at the onset they have to assume that you may need to cover the entire mortgage payment until the property is sold.
3). It is doubtful that the underwriter will allow any rent credit on a new purchase for much the same reasons listed above on your current residence. If the property is not a true multi-unit, no rental credit would be allowed in any case.
I am sorry to be so pessimistic about your financing options; however, I suggest you be far more conservative than the 3 times income "rule" (whoever made it up in the first place?). Your situation could be very dicey, very quickly if your co-owner did not pay the mortgage, the house doesn't rent, or the transfer goes awry. I am not trying to discourage you from your stated goals; however, it is important to be realistic about how underwriting may analyze your situation. I suggest you talk, at length, with a finance professional before making any final decisions. Obviously, if your income, savings and credit call support all of the payments for all of your goals my cautions are not necessary. One last thing: you will need to have six months reserves in savings (after buying the new property) for the rental property. Best of luck to you!