My husband’s stimulus check was taken for child support. I’m filing jointly this year. Since we did not get that money, are allowed to claim that as a recovery rebate?

No.

If your husband's first stimulus check was offset for child support, it is considered that he received it and applied it to child support.

On your 2020 return, he must indicate that he received the first stimulus check.

Thank you, I understand. But what if they took my child’s $500 stimulus payment to and applied it to my husbands past due child support. Can I claim my child’s $500 as a recovery rebate since I did not get that either?

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@Lynn1nn wrote:

Thank you, I understand. But what if they took my child’s $500 stimulus payment to and applied it to my husbands past due child support. Can I claim my child’s $500 as a recovery rebate since I did not get that either?

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No, because it WAS received and used to pay his bills.  You cannot claim the same money twice.

There is no "his" or "yours" on a joint tax return.