The TurboTax program will specifically ask if either tax filer has foreign investments such as bank accounts, trusts, etc. Obviously, that question will be answered yes and you'll fill in the details the program will ask for.
Should we report anything put into the joint account as a gift
What gift? I don't see any gift here. What I see is a married couple saving up to purchase a house. There is no gift here.
Special note here, as I don't know the specifics of your particular Non-Resident status and I'm not at all familiar with the rules for NR's when it comes to taxes. All I do know is that a non-resident alien can not use TurboTax because an NR has to file IRS Form 1040-NR. But you're married to a U.S. citizen so I honestly don't know what does or does not apply to your situation. Unless you've dealt with this on tax reporting in past tax years, you two will need to do some research on this, as I'm just not well versed on that part.