Does the Church allow for the use of contraception when a pregnancy would seriously jeopardize a woman's health?

The deliberate use of contraception on the part of spouses to prevent a pregnancy is never licit (CCC 2399).

Humanae Vitae states:

Neither is it valid to argue, as a justification for sexual intercourse which is deliberately contraceptive, that a lesser evil is to be preferred to a greater one, or that such intercourse would merge with procreative acts of past and future to form a single entity, and so be qualified by exactly the same moral goodness as these. Though it is true that sometimes it is lawful to tolerate a lesser moral evil in order to avoid a greater evil or in order to promote a greater good, it is never lawful, even for the gravest reasons, to do evil that good may come of it—in other words, to intend directly something which of its very nature contradicts the moral order, and which must therefore be judged unworthy of man, even though the intention is to protect or promote the welfare of an individual, of a family or of society in general. Consequently, it is a serious error to think that a whole married life of otherwise normal relations can justify sexual intercourse which is deliberately contraceptive and so intrinsically wrong. (HV 14)