I'm going to lay out my evidence because I have to 100% disagree with the stance that Mineo wasn't underboss during the 1960s. I also strongly disagree that the underboss position needs to be an active buffer. That is typically how it functions but it is not necessarily always true (e.g., the Bonanno family functioned without an underboss from 1979 to 1984; Pasquale Martirano was terminally ill and could do little in terms of active involvement when he was made the underboss in Philadelphia in 1990; Ignazio Denaro was Philly underboss in the 60s but was less active than capo Phil Testa who functioned as a de facto second-in-command in the family; Salvatore Vitale had responsibilities gradually stripped away from him as underboss). The evidence that Mineo was the underboss is very compelling and it's the same evidence that has Franzese as a capo during that period:

30 March 1964:
Scarpa spoke with James Rubertone (acting capo for Ambrose Magliocco) and was told that Colombo will be named the new boss and Mineo the underboss
The capos had been asked to survey their soldiers to find out their opinions on Colombo and Mineo
Scarpa told him that he thought Colombo and Mineo were a good selection

05 April 1964:
A ceremony was held to to install Colombo as the boss and Mineo as the underboss
Capos in the family attended the ceremony as well representatives from seven other families (including Detroit)

11 June 1964:
A meeting was held to introduce the capos in the family to the members who would be reporting direct to Colombo
Scarpa attended the meeting as a member of Colombo's regime and identified Mineo as the underboss and Franzese as a capo

05 January 1965:
It was reported that Carmine Persico was reported to capo
Mineo, while serving as underboss, was also responsible for a crew that included Anthony Abbatemarco, Anthony Ricciardi, Joe Yacovelli, Allie Giannattasio and James Cordella
Persico was given control of this crew due to Mineo's poor health

31 August 1967:
Scarpa reported that Franzese, still a capo, was lying very low and that Mimi Scialo was serving as his acting capo (Franzese also did not attend Colombo's son's wedding in December 1967 due to law enforcement heat)

04 December 1968:
Scarpa attended a party held for capos and members of Colombo's regime
Mineo attended and was once again identified as the underboss

07 July 1971:
Scarpa advised that a meeting was recently held in the wake of Colombo's shooting
Mineo, Joe Yacovelli, Carmine Persico, Joe Iannaci, Nick Bianco, Rocco Miraglia, Vinny Aloi, Jiggs Forlano, Duke Santoro, Mimi Scialo and possibly one or two others attended
Mineo was once again identified as the underboss at the time of this meeting
Mineo was asked to become the acting boss but turned it down, citing his age and health
Yacovelli then became the acting boss

Also, prior to Colombo's shooting, Scarpa identified Mineo as the underboss and that he had attended IACRL rallies

In October 1967, an FBI report laid out the hierarchy of the Colombo family as follows:

Joseph Colombo (Boss)
Charles Mineo (Underboss)
Benedetto D'Alessandro (Consigliere)
Vincent Aloi (Capo)
Simone Andolino (Capo)
Harry Fontana (Capo)
Nicholas Forlano (Capo)
John Franzese (Capo)
Frank Fusco (Capo)
John Misuraca (Capo)
Salvatore Musacchio (Capo)
John Oddo (Capo)
Carmine Persico (Capo)
Nicoline Sorrentino (Capo)