You should definitely enter the 1095-A info on your tax return, since you are the covered individual. When you signed up for the insurance, you probably indicated you were married and gave both your names, and expected income. You may want to reach out to the Marketplace for further clarification.
Why are you filing separately? This is usually not advantageous for a married couple. You may want to test your results both ways.
Since you are filing as Non-Residents, reach out to Sprintax to prepare your returns.
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