The central characters of the novel are the three friends - Jim, the narrator, George, William Samuel Harris and the dog, Montmorency - are themselves delightful sketches. Jerome K Jerome very thinly disguises himself as H and speaks to us through the novel. They enjoy their holidays rowing down the Thames. 
The novel does not have a story to tell. It does not really have one central character who could be termed 'the hero' or the 'heroine'. It is rather the river Thames itself that binds the novel together. The novel is a series of anecdotes.