In the book "Three Men in a Boat", the relationships between the characters J, George, Harris, and their dog Montmorency play a central role in the humor and story themes. The deep friendship marked by playful humor, teasing, and camaraderie reflects the dynamics of close friendship, showing the joys and frustrations of shared experiences. The boat trip serves as a backdrop to their relationship and highlights how their different personalities lead to humorous clashes and moments of togetherness. Montmorency, the dog, further enriches their bond, symbolizing the chaotic yet delightful nature of their shared adventures.