You may apply as married with ITIN for your spouse/kids. I did it once 10 yrs back. you attach the ITIN with Tax documents and mail it to IRS.

https://www.irs.gov/individuals/individual-taxpayer-identification-number

What is an ITIN?
An Individual Taxpayer Identification Number (ITIN) is a tax processing number issued by the Internal Revenue Service. The IRS issues ITINs to individuals who are required to have a U.S. taxpayer identification number but who do not have, and are not eligible to obtain, a Social Security number (SSN) from the Social Security Administration (SSA).

What is an ITIN used for?
IRS issues ITINs to help individuals comply with the U.S. tax laws, and to provide a means to efficiently process and account for tax returns and payments for those not eligible for Social Security numbers. They are issued regardless of immigration status, because both resident and nonresident aliens may have a U.S. filing or reporting requirement under the Internal Revenue Code. ITINs do not serve any purpose other than federal tax reporting.

An ITIN does not:

Authorize work in the U.S.
Provide eligibility for Social Security benefits
Qualify a dependent for Earned Income Tax Credit Purposes
Do I need an ITIN?
Does the following apply to you?

You do not have an SSN and are not eligible to obtain one, and
You have a requirement to furnish a federal tax identification number or file a federal tax return, and
You are in one of the following categories:
Nonresident alien who is required to file a U.S. tax return
U.S. resident alien who is (based on days present in the United States) filing a U.S. tax return
Dependent or spouse of a U.S. citizen/resident alien
Dependent or spouse of a nonresident alien visa holder
Nonresident alien claiming a tax treaty benefit
Nonresident alien student, professor or researcher filing a U.S. tax return or claiming an exception