You will generally file as "married filing separately" and report only your own income and deductions. You must indicate your spouse is a non-resident alien, as indicated in the other answer.
You have the option of treating your spouse as a US resident for tax purposes. This will allow you to file as married filing jointly, and claim your children as dependents. Joint filing using has lower tax rates than filing separately. However, if you treat your spouse as a US person, your spouse must report all their world-wide income on your joint US tax return and pay US tax on it. Your spouse may be able to claim a US tax credit or deduction if they pay taxes on the same income in their home country. You can also make this election to treat your children as US persons and claim them as dependents, but because they do not have social security numbers, you can only get a $500 per child credit for "other dependent" and not the $2000 per child child tax credit. To file a joint return and claim the dependents, you must file by mail, and you must include a W-7 form (application for International tax ID number, or ITIN) for your spouse and each child, along with any required proof.
Because of the issue with your spouse's foreign income being taxed in the US, you will have to carefully consider whether or not to file jointly. See articles below for details.
https://www.irs.gov/individuals/international-taxpayers/nonresident-spouse
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-credits-deductions/file-taxes-spouse...
