You answered:

Can I e-file with a foreign address?

Yes, you can now file federal (IRS) returns if you or your employer has a non-U.S. address. However, there are some restrictions regarding foreign-address returns:

• IRS regulations require a U.S. bank account to receive your tax refund, and you'll need a U.S. bank account 
• Like many stateside merchants, we require a U.S. billing address to pay for TurboTax if using a credit or debit card.
  • If you're deducting fees from your refund with the optional Pay With My Refund service, you'll need a U.S. or APO/FPO/DPO address.

OK...

I am a US citizen living abroad. Since I live abroad, my address is NOT a US address even though I do have a US bank account. 

Both payment methods for TurboTax mentioned above say I require a US billing address. I do not have a US address as I live abroad. Therefore, it seems impossible to file via TurboTax via a foreign address for anyone who is not military or US civil servant.

What am I missing?

Please state clearly that US citizens living abroad with no US address are unable to use TurboTax.