He held the rank of archbishop while serving as a nuncio in the diplomatic service of the Holy See from 1969 to 1997.
On 11 June 1969, Pope Paul VI appointed Barbarito Apostolic Nuncio to Haiti and named him titular archbishop of Fiorentino.
He received his episcopal ordination from the hands of Cardinal Amleto Giovanni Cicognani, with co-consecrators Archbishop Agostino Casaroli and Bishop Pasquale Venezia.
On 21 January 1986 Pope John Paul II named him Apostolic Pro-Nuncio to Great Britain.
[5] Barbarito was appointed an Honorary Knight Grand Cross of the Royal Victorian Order (GCVO) by Queen Elizabeth II in 1996.