Yes, TurboTax can handle filing your return and you can use the regular TurboTax version. You can start with the TurboTax Free version but you will be prompted to upgrade to the self-employed version.
You have the option to file married filing separately. You will leave the SSN field bank. You won't be able to e-file and need to print, write "NRA" for the spouse's SSN and mail your tax return.
Or you can file married filing jointly and treat your husband as a resident for tax purposes but then his worldwide income would be taxable in the US. Please see Nonresident Alien Spouse for details. You would have to apply for an Individual Taxpayer Identification Number (ITIN). You will have to print and submit the tax return with the ITIN application.
[Edited 3/7/2020 | 9:15 PST]
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