Yes. Unemployment insurance generally is included in your gross income and is taken into account in determining eligibility for premium tax credits. Recently, the CARES Act provided for an emergency, temporary increase in unemployment benefits of $600 per week, in response to the COVID-19 pandemic.
When applying for premium tax credits in the Marketplace, be sure to include information about your unemployment benefits, including the emergency $600 per week increase.
Note, however, that if you are applying for Medicaid or CHIP, the emergency $600 per week increase in unemployment benefits will NOT be counted as income in determining your eligibility for those programs.