Heinz' two younger brothers, Marcel von Allmen and Otto von Allmen were also ski champions. Marcel was two-time winner of the Lauberhorn (1941 and 1944). Otto was 10 times Swiss ski champion, three times winner of the Lauberhorn, and champion of the Nordic/Alpine combined in 1944. The three brothers won 19 Swiss ski championship races, 19 Lauberhorn races, 4 World Championship races. In the period leading up to, and during, World War II, the brothers (along with Hans Schlunegger, also of Wengen), were champions in the combined Nordic/Alpine disciplines, which were dropped after the war because of the difficulty of training for all four events.