Liz Miller is a 29-year-old graduate student at the University of Notre Dame, a private school with strict adherence to Catholic teachings against contraception. Because of that, her doctor at the university can't prescribe birth control, and when she obtains the prescription from another doctor, her insurance from the university won't cover it.
There is an accommodation in place through the Affordable Care Act for situations like the one Miller faces. The accommodation allows religiously affiliated nonprofits to sign a form certifying their objection. The insurer will then directly cover the cost of the birth control. However, Notre Dame says that signing the opt-out form violates their religious liberty because the outcome is still the same - contraception is distributed.
This article has more on the issue. The situation is one that could have ripple-effects for religious nonprofits and their employees across the nation.