Albeck graduated from Chenoa High School in Chenoa, Illinois and received his bachelor's degree at Bradley University in 1955 and his masters at Michigan State University in 1957. He married Phyllis L. Mann in 1952 and they have five children.
He was the head coach of the Denver Rockets during most of the 1970–1971 season. The Rockets had begun the season under head coach Joe Belmont, but Belmont was fired after the team lost 10 of its first 13 games. Albeck replaced Belmont as the Rockets' head coach. The Rockets went 27–44 under Albeck to finish the season with a record of 30 wins and 54 losses. They tied the Texas Chaparrals for fourth place in the Western Division (28 games behind the Indiana Pacers) and on April 1, 1971 lost a one-game playoff to the Chaparrals, 115–109, to determine who would advance into the ABA Western Division semifinals. During the season Denver's average home attendance dropped to 4,139 fans per game from 6,281 the year before. One week after the playoff loss, on April 8, 1971, Albeck was replaced by Alex Hannum as Denver's head coach. Hannum resigned as coach of the San Diego Rockets to become the Rockets' head coach, general manager and president. Albeck then became player personnel director for the Rockets.
During the 1972–1973 season Albeck was an assistant coach for the San Diego Conquistadors under head coach K.C. Jones. Albeck also served as director of player personnel for the Conquistadors. During most of the 1973-74 he served under 'Ques' head coach Wilt Chamberlain. Chamberlain missed a few games, during which Albeck filled in as the Conquistadors' head coach, winning all of them.
Albeck was an assistant coach for the Kentucky Colonels during the 1974–1975 season in which the team won the 1975 ABA Championship. Albeck returned as an assistant coach with the Colonels during their final season in 1975–1976.
From 1986 through 1991 Albeck was head coach for Bradley University, his alma mater. He is a member of the Sigma ChiFraternity, as well as a Significant Sig and a member of their Significant Sig Hall of Fame.
His all time coaching percentages is .535 for his 7 years as a head coach in the NBA.
After serving as an assistant coach for the Atlanta Hawks, Albeck was as an assistant coach for the Toronto Raptors in 2001 when he suffered a debilitating stroke, which left him partially paralyzed. He has been in rehabilitation since then.