Is it permissible for my husband to take me back after he divorced me three times with a single utterance while he was angry, and we have an infant child, knowing that he is aware of and understands what he did, and is this divorce considered a single divorce?

Divorce pronounced during extreme anger is not valid, and a triple divorce counts as a single one. As long as the divorce occurred during extreme anger, nothing counts, and you do not need a new return or a new marriage contract.

If a triple divorce is counted as one, and it was the first or second divorce, it is a revocable divorce (ṭalāq rajʿī). The husband can take his wife back during her waiting period (ʿiddah). If the waiting period ends without him taking her back, then a new marriage contract is required.