I'm on the same boat, wife holds ITIN (applied in 2011 with H4) and SSN (applied in 2017 with Green Card) but always use ITIN to file tax. I don't even know that ITIN holder is not qualified for getting the stimulus check (they're taxpayer!) until today because IRS Get My Payment portal do allow people to enter ITIN number.
Anyway, I found this answer online:
https://youtu.be/YFzI5lGlWCY?t=277
