Balin was born in Brooklyn, New York to Jewish parents. Her father, Sam Rosenberg, was a dancer, singer and comedian who worked the Borscht Belt. He later quit show business to join his family's furrier business. Her mother was a Hungarian-born professional dancer who escaped a troubled family life by marrying at age 15. Sam Rosenberg was her third husband by age 21. They too divorced when Ina and her brother, Richard Balin, were still quite young. The siblings were placed in boarding schools until their mother married a fourth time, then to shoe magnate Harold Balin, who later adopted Ina and Richard. Balin graduated from high school at age 15 after having spent five years at a boarding school in Pennsylvania.
Balin did summer stock, which led to roles on Broadway. She first starred on Broadway in Compulsion, portraying Ruth. In 1959, she had the role of Alice Black in the comedy A Majority of One.
Film
In 1959, Balin landed her first film role in The Black Orchid. She was Paul Newman's love interest in the 1960 screen adaptation of From the Terrace. In 1961, she appeared as Pilar Graile in The Comancheros with John Wayne and Stuart Whitman. Co-starring with Jerry Lewis in the 1964 hit comedy The Patsy, Balin also had a secondary part in 1965's The Greatest Story Ever Told. She also co-starred with Elvis Presley in his 1969 film Charro! She co-starred in the 1971 filmThe Projectionist. She also co-starred in the 1982 comedy The Comeback Trail, and she appeared in The Young Doctors, the 1961 hospital drama with Ben Gazzara, and Fredric March.
Humanitarian activities
In 1966, Balin toured Vietnam with the USO on the first of many trips to the war-torn region. In 1975, she aided in the evacuation of orphans during the fall of Saigon. Eventually, she adopted three of these orphaned children. In 1980, she played herself in a made-for-television movie based on her experiences, The Children of An Lac. While working on The Children of An Lac, she became acquainted with Christy Marx who, at the time, worked as a producer's liaison for various television programs. According to Marx, she used Balin's story as a basis for a character in the animated show Jem when she became a writer. The character of Ba Nee is based on Balin's adopted daughter, Ba-Nhi. Ba Nee's obsession with and struggle to find her birth father are the focus of several episodes of Jem.
Death
Balin, a former cigarette smoker, died on June 20, 1990 at Yale–New Haven Hospital in New Haven, Connecticut, aged 52, from complications of chronic lung disease, including pulmonary hypertension. She had been at the hospital seeking a lung transplant. A single mother, she was survived by her father, Sam Rosenberg; her three adopted children: Nguyet Baty, Ba-Nhi Mai, and Kim Thuy; a brother, Richard Balin; and two grandchildren. Ba-Nhi Mai and Kim Thuy were raised by Hollywood talent agent Ted Ashley and his wife Page.