Her father, David Giladi (born in Transylvania, Austria-Hungary), was a journalist, novelist, and translator, as well as one of the founders of the Israeli newspaper Maariv.
In Lapid's book Veulai Lo Hayu she documents the story of her father's immigration to Israel, his integration into Israeli society, and her own childhood in Tel Aviv during the 1930s and 1940s.
They had three children: Michal (who was killed in a car accident in 1984), Merav, and Yair – a well-known Israeli politician, novelist, journalist and television personality, formerly Prime Minister of Israel.
She writes historical novels, realistic prose addressing social issues and ethnic discrimination, and several detective novels.Gai Oni (1982) is the story of the Galilean village that became Rosh Pina.
Badihi is a journalist of a Beersheba local newspaper called "HaZman Darom" (literally "The Southern Times"), and in each book she stubbornly insists on dealing with a detective mystery no one asked her to solve.