Elizabeth Weber has "great" memories of her marriage to Billy Joel

She told PEOPLE: "It was great then, it's great whenever I think about it, and it's great now."

Elizabeth has revisited that part of her life as part of the Billy Joel: And So It Goes documentary and admitted that it was the two-parter's ex ecutive producer Steve Cohen who persuaded her to get on board.

"I love Steve and I worked with him, and he's a close friend of mine...but I thought, 'Wait a second. I have a really nice life. I have a lot of privacy. I immediately [agreed]."

It was then that director Susan Lacy approached Elizabeth and because she did it in such a "personal way", she admitted that the whole thing "felt right" for her to commit to.

"Susan approached me in a very personal way, and it resonated with me, and Billy licensed the music, so I knew that there would be good music.

"So it felt right - and it still does."

Steve also noted that he and Elizabeth have a long-standing friendship and even though there was some "reluctance" for her to sign onto the documentary after such time away from the spotlight, he knew she had to do it.

He said: "Elizabeth and I have a friendship that has lasted since we first met.

"She was there at the very beginning when I got hired, and...I will tell you, there was reluctance in the beginning because she's been out of the public eye and she's been maligned incredibly in the blogosphere.

Following his marriage to Elizabeth, Billy went on to tie the knot with model Christie Brinkley in 1985 and has Alexa, 39, with her but they split a year later.

He was then married to author Katie Lee from 2004 until 2009 but then tied the knot with Alexis Roderick in 2015 and has daughters Della and Remy with her.