You have two options.
1. File as married filing separately. You will need to use a fake SSN for your spouse to get through the interview. You can't e-file. Print your return, cover the fake SSN with white-out and write "NRA" over it, and file by mail.
2. You can choose to treat your spouse as a US resident and file jointly. Doing this means that all her world-wide income for the whole year must be reported on the return and taxed by the US. She can claim a deduction or credit for taxes that she pays on the same income to overseas governments, which will reduce the effects of double-taxation but might not eliminate it completely. You would have to test it out to see what happens.
To file jointly, your wife needs an ITIN, international tax ID number. The IRS won't process an application for a tax number unless it is attached to a joint tax return. So what you need to do is prepare a form W-7 application for ITIN, along with your joint tax return, print them both, and mail them to the address in the W-7 instructions. Be sure to include any required proof of identity for the W-7. You will likely need your spouse's original signatures as well, so you will either need to bring your tax papers with you next time you visit each other, or use an express service to send them back and forth, and if you can't get the paperwork done by April 15, be sure to request an extension.
Once the IRS processes the W-7 and issues the ITIN, they will forward the tax return for processing.
