If you mean by 'stay' to live with your husband's family then no, this isn't required. In fact it is obligatory upon the husband to provide a suitable accommodation for his wife in order for her to feel safe and comfortable.
Living with in-laws can be an option for the newly married couple who have just gotten on their feet, however it has been shown many times that that long term living with in-laws can cause many problems as well as a lack of privacy for the couple. Therefore it is recommended that the couple try to eventually find their own place.
May Allah grant you success