Suhey was the MVP of the 1948 Cotton Bowl Classic. It has been suggested Penn State's now-famous "We Are Penn State!" stadium cheer has its origins in a statement made by team captain Suhey prior to that game. Suhey is said to have declared, “We are Penn State. There will be no meetings,” in response to SMU's request for a meeting to protest the participation of Penn State's two black players (Wallace Triplett and Dennie Hoggard).
Suhey married Virginia "Ginger" Higgins, a daughter of Bob Higgins, a former All-American at Penn State and Suhey's college coach. Three of their sons, Larry, Paul, and Matt, were letterman at Penn State from 1975–1979. Matt would go on to play 10 seasons in the NFL with the Chicago Bears. One grandson, Kevin Suhey, was a quarterback and special teams player for the Nittany Lions from 2005–2007 and another grandson, Joe Suhey, was a running back for Penn State from 2007–2010. The Higgins-Suhey family has been called the "first family of Nittany Lion football", with 90 years of involvement with the Penn State football program.