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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
This husband incurs a huge sin for his stance. Allaah Almighty says (what means):
• {O you who have believed, protect yourselves and your families from a Fire ….} [Quran 66: 6]
• {Men are in charge of women by [right of] what Allaah has given one over the other ….} [Quran 4: 34]
Since a husband is responsible for his wife, he is not allowed to let her be seen without the Sharee'ah-approved Hijab.
Allaah Knows best.