Last time I applied for a mortgage I asked the loan officer about this. They advised that on a joint application they take the "lower middle" score. What that meant was they would get credit scores from the three major (US) credit bureaus, for both me and my cosigner, discard the highest and lowest for each of us and then settle on the lower of the remaining two.
Bureau | Signer's score | Cosigner's score
Equifax | 730 | 680
Experian | 740 | 710
Transunion | 750 | **700**
Signer's middle score is 740, cosigner's middle score is 700. So, the lower middle score is 700.
I'm not sure if all loan companies use this method, but mine advised it was pretty common method among the big mortgage providers at least.
If the company you quote with uses this method, you can be sure that the lower credit rating of your co-applicant will mean they base their offers on her score, not yours. But it will be her middle score, not her worst. Usually all three bureaus report a similar score for any particular individual anyway so this factor doesn't make a huge difference, but it might help a bit, especially if one of the bureaus has errors on your report and the other two don't.
If you have sufficient income to qualify for the mortgage you need on your own, you'd probably be better off applying on your own. A higher score will qualify you for better rates, and for something big and long term like a mortgage every fraction of a percent difference can translate into hundreds of dollars over the life of the loan.
If you can't qualify for the mortgage on your sole income then it's a moot point, you'll have to include a cosigner. However, there are steps you can take that will provide an almost immediate boost to your girlfriend's credit score; most notably, paying down revolving debt. If clearing all credit card debt is not possible right now, try to at least re-balance things so that each revolving account is using a similar percentage of its respective credit line (as opposed to some small balances and some maxed out). And the more you can bring down utilization overall, the more the score goes up. Doing this right before the end of a credit card billing cycle (i.e. don't wait for the statement to arrive - the balance will already have been reported by then) will ensure a lower balance being reported to the bureaus (note, a minimum payment will still have to be made after the statement is generated, so if you're budgeting, reserve some for that payment too).