Picon and Kalich adopted their first child, George Weinstein, in 1941. Matched with this Belgian Jewish orphan through The foster care agency, an organization designed to help the child victims of war, George was already a teenager at the time of his "adoption." He remained in London, where Picon and Kalich underwrote his education until the family was reunited in 1949.

In 1954, they adopted their second child while performing in Israel. Meira, the daughter of Picon's deceased stepbrother by her father's first wife, was also fully-grown at the time of her adoption. The couple adopted their third child, Dov Steiner, in 1965. While all three of their children were nearly adults at the time of their adoption, Picon and Kalich were deeply invested in their children's well being. They visited with them frequently and kept up a close correspondence throughout their lives.