Albanese was one of the most beloved sopranos in the Italian repertoire, specializing in roles that suited her physical and vocal appearances of vulnerability and delicacy. She specialized in Puccini, and was associated with his Madama Butterfly more than with any other role. Her voice was smallish and not always precise in pitch, and could turn edgy under pressure, but nonetheless, her vocal and dramatic intensity and sense of apt staging made her performances riveting.
She first studied piano, but switched her energies to voice, studying with Giuseppina Baldassare-Tedeschi. She won the Italian National Singing Competition in 1933, and her opera debut, as Butterfly, was as a mid-opera last-minute substitute for an ailing colleague at the Teatro Lirico in Milan, in 1934. Her La Scala debut was in 1935 as Lauretta in Puccini's Gianni Schicchi, her Covent Garden debut as Liu in Turandot, and her Met debut was in 1940 as Butterfly, beginning an association with that house that lasted until 1966. She made the occasional forays into heavier repertoire during her career, even experimenting with the role of Elsa in Lohengrin in her early years in Italy, but rarely added such roles to her repertoire, and being careful with her performances of even such medium-weight roles as Tosca, though towards the end of her career, with little to lose, she performed heavier roles such as Aida.
After her retirement, she remained active, leading the Puccini Foundation (which she and her husband created), teaching master classes at the Juilliard School of Music and Marymount Manhattan College, and directing operatic scenes. In 1985 and 1987, she made cameo appearances in Steven Sondheim's Follies. In 2000, she received the Handel Medallion. The honor, which was bestowed upon her by Mayor Rudolph W. Giuliani, is a tribute to individuals who have enriched New York City's cultural life.