No, when spouses file jointly, both spouses must have valid SSNs to receive a Payment with one exception. If either spouse is a member of the U.S. Armed Forces at any time during the taxable year, only one spouse needs to have a valid SSN.
If spouses file separately, the spouse who has an SSN may qualify for a Payment; the other spouse without a valid SSN will not qualify.
You will be able to claim the payment when you file your 2020 tax return if you both file with a SSN. Filing with the ITIN is only preventing you from receiving the advance payment.
Stimulus payments will be based on information from your most recent tax filings, either 2019, or 2018 if you haven't filed this season yet. But, the amount paid to you now will be reconciled on next year’s tax return based on your current 2020 situation.
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