As early as 1476, the Barbarigo family had been affiliated with the Templars, with members of the family regularly attending Templar meetings in Rome. During one of these meetings, they expressed worry over the Assassin Giovanni Auditore da Firenze.
The Barbarigo remained with the Templars after the execution of Giovanni Auditore and two of his sons, Federico and Petruccio, and following the failure of the Pazzi family to overthrow Lorenzo de' Medici of Florence and take control of it, the family was involved in the plot to take control of Venice, instigated by the Grand Master of the Order, Rodrigo Borgia.
Despite the death of Emilio Barbarigo in 1485, at the hands of Ezio Auditore, the son of Giovanni, the Barbarigo family remained steadfast. That same year, following the assassination of Doge Giovanni Mocenigo by the Templar Carlo Grimaldi, Marco Barbarigo assumed the title of Doge; a point of much contention among his fellow Templars.
Their joyous time was short-lived however, as Marco was assassinated during the Carnevale, subsequently being replaced by his brother Agostino, a friend of the Assassins. Not long afterwards, Ezio sided with the Venetian Mercenaries Guild and assaulted the city's military district, which had remained under the control of Silvio and his servant Dante Moro.
As the leader of the mercenaries, Bartolomeo d'Alviano distracted the Templar soldiers, Ezio managed to sneak into Arsenale di Venezia and eliminate Silvio and Dante, seemingly ending the Templar presence in Venice.