"Between the Devil and the Deep Blue Sea" is an American popular song published in 1932, with music by Harold Arlen and lyrics by Ted Koehler, and first recorded by Cab Calloway in 1931. It was introduced in the 1931 Cotton Club show Rhythmania and is now a widely recorded standard.

Based on this passage, who wrote between the devil and the deep blue sea? Let's give stream of consciousness first:
To answer the question, consider the following: "Between the Devil and the Deep Blue Sea" is an American popular song published in 1932, with music by Harold Arlen and lyrics by Ted Koehler, and first recorded by Cab Calloway in 1931.
So, the final answer is music by Harold Arlen and lyrics by Ted Koehler.