All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
However, if your husband wants to be kind to that child and look after him, then he may do so, as this is a voluntary act of worship and Allaah loves those who are kind to others. Therefore, you have no right to prevent him from being kind.
Nevertheless, he has to be careful not to fall into temptation with the child's mother as a consequence of his kindness to the child. There is nothing better than staying on the safe side when it comes to religion.
Allaah Knows best.