Police discovered Michael Greaney, 53, and his wife, Valerie, 49, at their home in Cobh, Co Cork.
Their eldest daughter Michelle was found lying in the street after trying to flee the house.
Officers are not looking for anyone else in connection with the incident.
Bishop of Cloyne, Rt Revd William Crean, said: "I was deeply shocked to hear of the deaths of Michael and Valerie Greaney and the serious injuries suffered by their daughter, Michelle.
"I ask the faithful of the diocese to pray for all of those affected by these sad events.
"May the light of Christ, whose coming into the world we celebrate at Christmas, help to guide us through this great darkness which has fallen on the community of Cobh, and on the diocese as a whole."