Yes, this. I believe the Catholic church makes exceptions for this. I know that in medical conditions where one needs birth control pills (say, big fibroids, endometriosis) it is allowable to use them, since the primary use is medical, not because a couple didn't want children.
For all the other posters mentioning super strict NFP.....when does the health risk outweigh birth control being bad? I'm pretty sure that there is that option out there.
Also, complete abstinance, as another poster mentioned, sex is not just for procreation. So abstaining would technically be sinful in that case, since sex is important in a marriage outside of procreation.
This is not an accurate summary of Catholic teaching. While the church does make allowances if the birth control itself would resolve a healthy problem, her husband's vasectomy will not cure the OP. While the couple certainly has grave reason to avoid having more children and is certainly not acting in selfishness, just because they do not want children, the action of the vasectomy would be to prevent children rather than to treat a health problem. I understand that many of you on this forum view this differently, but in the eyes of the Church, this is how it is. Abstinence is the only Catholic response to the need to prevent pregnancy. The extent of this abstinence (NFP, strict NFP, post-ovulation only + added days, or even total abstinence) is a decision for the couple as part of their call to responsible parenthood. Complete abstinence would not be sinful in this case while a Catholic couple resorting to birth control would be considered sinful. I admit that it is hard to understand, and many disagree with the official Catholic teaching that complete or almost complete abstinence would be allowable under the principle of double effect while birth control would not. As the last poster pointed out, the fact that the OP's Protestant husband views this differently than the Catholic Church is what complicates this.
But it IS treating a health problem. If mother gets pregnant, she dies. The OP and her husband would love more children. But to do so will likely lead to death.
How is this any different from the case of removing the fallopian tube during an ectopic pregnancy? If a woman has 2 ectopics and loses both tubes, she is, in effect, sterilizing herself at the same time she is saving her life. Why would this be any different? If there is no form of sterilization, then both mother and baby die. Or would it be more acceptable for her to get a hysterectomy while pregnant, following the ectopic principle? Not being snarky, truly curious. To me, this is a grave condition, one that would be allow birth control.