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.
We have already issued Fatwa 88099 clarifying that it is permissible for a woman to go out of her home for her need with the consent of her husband provided that she abides by Islamic conditions, like wearing Hijab, not beautifying herself and the like.
However, what your husband mentioned that it is an obligation on the wife not to go out of her home at all is not correct and his quoting as evidence the verse in Chapter Al-Ahzaab [Quran 33] is not a correct deduction. The verse means that they should stay in their houses and not go out without a need, and the wives of the Prophet who were personally addressed in the verse – and the Muslim women to whom this verse also applies – used to go out for their need. They used to go to the prayer in the mosque, and it is confirmed that the Prophet said: “Do not prevent the female servants of Allaah from going to the mosques of Allaah, but they should go out having not perfumed themselves.” [Ahmad]
Also, the Prophet said to Sawdah (his wife) : “Allaah has given permission for you (i.e. the Prophet's wives) to go out to fulfill your needs.”
This is evidence that going out is not absolutely forbidden, but a wife is not permitted to go out of the house of her husband without his permission unless there is a necessity to do so, or that she has a need that requires her going out and which she could not achieve except by going out.
Allaah Knows best.