The new book, titled "Cher: The Memoir (Part One)," details the turbulent aspects of her and Sonny's union ... she confesses she was so unhappy at one point, she considered taking her own life by jumping from the balcony of a Las Vegas hotel room.

Per Cher, while she and Sonny stayed at the Sahara Hotel in October 1972, she revealed to SB her unhappiness ... and told him she desired to sleep with their guitarist, Bill.

Though Cher wrote that she didn't actually mean it, she felt this was the only way to get Sonny to take her breakup pleas seriously.

Eventually, the estranged couple -- who was breaking records with their show, "The Sonny and Cher Comedy Hour," at the time -- agreed to split up. However, Cher agreed to continue living with Sonny most days to preserve their public image.

During one of their mornings together, Sonny told Cher he had "seriously thought about throwing you off our balcony" after her Bill confession.

She added ... "He laughed a little at that and so did I. It was crazy that he was telling me ... He went on: 'I figured I’d plead insanity like Spade Cooley and get seven years in jail before they released me. Then I’d get a book deal and my own show.'"

Cher said she responded to Sonny's blunt truth by saying "there would have been no need to push [her]" because she was "gonna jump" anyways. She called this conversation "the darkest moment" of their marriage."

She continued ... "I don’t think for a minute that Sonny would have actually pushed me off the balcony, but I’m sure it crossed his mind, and he knew that jumping off had also crossed mine. What else could we do but laugh?"

Sonny and Cher's marriage officially came to an end in 1975 after 11 years. The pair first met when Cher was only 16 and Sonny was 27 ... with Cher initially moving in with him as a cook and a housekeeper.