Mr Halappanavar has insisted that an abortion was refused during the miscarriage and at one point the couple were told it was because Ireland "is a Catholic country".
The parents told their daughter she could "continue to live in misery" in their home or she could "have the abortion and tell everyone it was a miscarriage, " the lawsuit added.
She died at a Galway hospital last October following a miscarriage amid controversy over her treatment and complaints she was denied an abortion on the basis that Ireland was "Catholic".