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 ask Allaah to exalt his mention as well as that of his family and all his companions.
One of the most important objectives of the Islamic Law is to multiply the progeny. It is indeed for this reason that Islamic jurisprudence legislated marrying a fertile woman. Therefore, it is forbidden to totally prevent pregnancy except in case of necessity. This is explained in Fataawa: 86253 and 83516. Therefore, if it is proven by trustworthy experienced doctors that getting pregnant is a danger to your life, and that it is an obligation to permanently cut off reproduction as a way of removing this danger, then in this case it is permissible for you to do so.
The ways of preventing pregnancy are various. Some means could transgress a religious limit or cause a physical harm, so one has to resort to the least harmful method.
However, it is forbidden for your husband to perform a vasectomy because the necessity is in relation to the risk of your becoming pregnant [and does not pertain to him], so it is not permissible for the necessity to exceed its limits to include others. So the ruling in relation to your husband remains as stated. For more details, please refer to Fataawa: 86967 and 84675.
Allaah knows best.