I too saw this film when I was a youngster and of course didn't understand most of it except that I loved the music and always remembered the main melody even after 50 years! The main attraction is the wonderful singing of Tito Gobbi, baritone, heard near the beginning when he sings the familiar theme song, with an accordion to accompany him. There's also the performance later on of the new opera "The Glass Mountain" and he is splendid in this as well.
Mostly the story revolves around a young married couple, Richard Wilder, as a music composer (Michael Denison) and his wife Anne (Dulcie Gray). In the aftermath of recuperating from a plane crash in war torn Italy Richard also meets Alida, a lovely Italian lady, and from her he learns about the legend of the Glass Mountain and seriously plans to write an opera based on it when he returns home. This opera would of course be written with his newfound friend in mind, Tito Gobbi, the baritone, as the central figure, and thank goodness for once a baritone is the hero! Let the tenors wait their next turn.
Eventually Richard must choose between a wife back home who loves him and the Italian new love who is devoted to him too. It is during the premiere of his new opera that events take a sudden turn when there's news of a plane crash in which his wife Anne was traveling in - this gives him the answer.
A very romantic film and beautiful music as well. An experience not to be missed.