A look into the bill text's wording shows that indeed, dependents would receive $2000 each:
"Section 6428A of the Internal Revenue Code of 1986, as added by the COVID-related Tax Relief Act of 2020, is amended by striking “$600” each place it appears and inserting “$2,000”, and by striking “$1,200” each place it appears and inserting “$4,000”."
This means that a family of four who earned less than $150,000 would receive $8,000 instead of $2,400. The money would also phase out at a higher earning bracket since the 5% reduction rule over the income limits didn't change. Read more