I think that the relationship between Elie and his father is portrayed in a very unique way throughout the work. On one hand, there are definite aspects of adolescent challenges within their relationship. This consists of being embarrassed at times by his father and sense of seeking to establish his own independence are present in Elie's connection to his father. Yet, there are some unique aspects within their relationship which are forced by the condition of the Holocaust. For example, the ending of the work, where Elie awakens one morning to find his father gone, and the sense of emptiness this creates is combined with the hollow reality caused by the inescapable presences of death and suffering. This is anything but typical in an adolescent relationship. At the same time, when Elie has to make consistent choices about whether to continue with his father, who is in ailing health, it represents a moment of choice that is different than most relationships between adolescent fathers and sons.
Elie and his father have a changing relationship in the memoir. At the beginning, their relationship is a typical older father--know-it-all son relationship. Elie's father doesn't have much use for Elie's interests (Cabbalism), and Elie sees his father as distant from him and nonchalant about the warning signs of the approaching deportation.
In the book's middle chapters, Elie and his father become equals. Elie, the physically stronger of the pair, ensures his own survival, and his father tries to encourage Elie emotionally and psychologically.
Finally, near the end of Night when Chlomo's health deteriorates, Elie takes over the "adult" role by caring for his father and making life-or-death decisions.
Ironically, in the midst of something as abnormal and horrific as the concentration camps and Holocaust, Elie and his father's relationship follows the typical pattern of most father-son relationships, just at an advanced speed, for many adults in today's society find themselves in roles of authority over their aging parents, providing for them physically and emotionally, just as Elie had to do for his father, even when he was just a teen.