Murnaghan emigrated to the US in the late 1860s, where he was a housebuilder and keeper of a livery stable in St Louis, Missouri.
He married Angela Mooney, originally from Dublin with whom he had 9 children.
Francis Dominic Murnaghan, the Irish mathematician, was his son, and Francis Dominic Murnaghan, Jr., a United States federal judge, was his grandson.
James Murnaghan, judge of the Supreme Court of Ireland, was his son.
Sheelagh Murnaghan, Ulster Liberal Party MP in Northern Ireland was his granddaughter.