This is of course a disaster waiting to happen, and it's doubtful you will have the influence to do anything about it unfortunately (if they've been together for 15 years and yet you barely know him). Hopefully they simply won't qualify and the problem solves itself.
To directly answer your question though:
If this was a multifamily home, or an investment property, a formal rent agreement would potentially allow you to use some percentage (up to 85% of the fair market rent I believe) of that rental income as her income. I'm not sure if there are restrictions on the relationship between the renter and the rentee -- which is to say I'm not sure if the rental income can come from a significant other or not.
However, I'm guessing it is neither of those things and she is instead buying a single family home she intends to have as her primary residence. In that case none of his income can be included for calculation of the debt to income ratio.
There are also gifting rules which determine where you can get the money for the down payment from. Depending on the circumstances of her credit score and so on it may be technically against the rules of the FHA loan to use his money for the downpayment as well. But at least in the pre-mortgage crisis days no one looked at where the money was coming from too closely, I'm not sure how stringent everything is today.
She should also realize that given how the economy works today, the flexibility renting provides is an enormous benefit that really should be translated into real dollars. Home ownership got such prominence in the baby boomers generation because buying makes a hell of a lot more sense when you expect to stay at one job for your entire career and aren't expecting to move for decades, if ever. It relates to my next point on amortization.
I also wanted to add something about amortization because loan officers take advantage of the fact that most people have no idea how they work. If she were to buy a $165,000 home on a 30 year FHA mortgage, she will be paying about $840 per month. But here's the thing: most people don't hold on to a 30 year mortgage for 30 years. It's more like 5-10 and probably closer to 5. This matters because it turns the whole "renting is throwing away your money" thing into a huge falsehood. Out of that $840, only about $220 is paying the principal and the rest is interest. You don't start paying more towards loan principal than interest until 15 years into the loan!
So lets say after 7 years you decide to upgrade, or move to a new city, or whatever. You would have paid about $70,000 and nearly $49,000 of it went straight to interest payments!
Talking about it from this approach might be more effective if you are hoping to dissuade -- the numbers people use when comparing buying vs renting are very often hugely massaged in favor of buying and don't take a lot of things into account (see also my comment on repair costs).