All perfect praise be to Allah, The Lord of the Worlds. I testify that none is worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
The supplication for entering the toilet is a recommended and not obligatory, so there is no sin on whoever does not recite it, and he will not be harmed, Allah willing.
If your husband has relieved himself at a place where people are not harmed by it, then there is no sin on him.
Allah knows best.