Avery was a veteran of stage, TV and film. He started his career in Chicago at the Goodman Theatre. He joined The Second City and later teamed with Jack Burns to form the comedy team of Burns and Schreiber. They recorded several comedy albums and appeared on numerous television shows.

Schreiber is remembered for his many Doritos ads, as well as his appearances in classic television shows. In 1965, Schreiber played the role of Captain Manzini on My Mother The Car, starring Jerry Van Dyke.

Schreiber was a regular guest star on Chico and the Man, starring Freddie Prinze and Jack Albertson. He was also a frequent star on the game show Match Game.

In 1994, Schreiber suffered a heart attack, which was brought upon by his diabetes. Though he survived triple bypass surgery, he never fully recovered.

Schreiber then died of a fatal heart attack on January 7, 2002, aged 66. He was residing in Los Angeles at the time of his death.