It´s often the consigliere of a family that settles beefs, or mediates disputes among the members. At least that was the case in the past. So he had to stay in contact with all members of the family.
The Underboss? I guess it depends on how big a family is. In the smaller ones, I think he is in contact with the soldiers a lot. But that is not the case when it comes to the bigger families with 100-250 members. The underboss (just like the boss) do take measures to shield himself from potential future mafia witnesses and informers. Especially nowadays.
The real power in a family is in the captains and above.
And I believe that some of the captains frequently meets with the underboss and the boss.