Answer
Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
The correct view is that the husband is only responsible for admonishing and advising his wife, but she will be held responsible for her deeds alone in front of Allah on the Day of Judgment.
Answering your question, Dr. Mohammad S. Alrahawan, Associate Professor at the department of Islamic Studies in English, Al-Azhar University, Egypt, states:
Allah has commanded husbands and fathers to take their responsibility of instructing and paying sincere advice to their wives and fellows. The Quran reads, “O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones, over which are [appointed] angels, harsh and severe; they do not disobey Allah in what He commands them but do what they are commanded.” (At-Tahrim 66:6)
The Prophet (peace be upon him) has further confirmed this responsibility in his hadith: “All of you are guardians and are responsible for your subjects. The ruler is a guardian of his subjects, the man is a guardian of his family, the woman is a guardian and is responsible for her husband’s house and his offspring; and so all of you are guardians and are responsible for your subjects.” (Al-Bukhari and Muslim)
But scholars differed on whether a husband will be held responsible for his wife in case she neglects fulfilling any of the duties due on her towards Allah.
The correct view is that the husband is only responsible for admonishing and advising his wife, but she will be held responsible for her deeds alone in front of Allah on the Day of Judgment. This is based on the Qur’anic statement, “And every soul earns not [blame] except against itself, and no bearer of burdens will bear the burden of another “ (Al-An`am 6:164)
For more, see these fatwas:
What Are the Requirements of Hijab?
Can Muslim Women Wear Colored Hijab? (Video)
Allah Almighty knows best.