It depends. You can only receive either the Lifetime Credit or the American Opportunity Credit up to a maximum of $2500 but not both.
I think what you may be referring to is that you are receiving the American Opportunity Credit and there is a non-refundable portion of the credit being applied as well as a refundable credit. This is referred to as a partially refundable tax credit.
With the AOC, up to 40 percent of the credit is refundable and counted as a tax payment. When you claim this credit for education expenses, Form 8863 separately calculates the refundable and nonrefundable portions. For example, if you calculate a $2,500 American Opportunity credit, a maximum of $1000 may be reported as a refundable tax credit with the remaining $1,500 reported as a nonrefundable credit.
If this doesn't fit your situation, please write back and let us know specifically on why you think your dependent is receiving both credits.
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