That's the solution I suggested in my first response. You both download from the joint accounts into your own separate versions of Quicken. The only complication comes when the categorization of the entries is not automatic. You would each have to input categories for those uncategorized transactions. But keep in mind, the uncategorized transactions should diminish with each download. The first time you categorize a transaction at, say, Goodyear Tire Shops as "automotive," the next time you download a check to them, it should automatically show up as "automotive." What you might consider doing is downloading from the bank, categorizing those that haven't been categorized and then print out a ledger for your GF. Give it to her, have her download into her quicken, and then when she has to categorize, she can work from your list. (I have another complicated work-around that's percolating in my brain. I'll tell you about that one later.)
Now, I'm still confused. When you say "her bank" in the quote above, is that one of the banks where the joint account is held? Same question when you say "mine." I thought these were joint bank accounts. As a result, I'm confused by the distinction between her bank and your bank. If you're talking about accounts other than the joint accounts, the download ability is irrelevant. You only need to be able to download from the banks that have the joint accounts, so that each of you can download transactions into your own version of Quicken. For all of the other accounts (the non-joint ones) you can input manually, download, or whatever.