First things first. I do not think Jane Eyre is an utterly melodramatic novel. It is more the Victorian emphasis on emotions or feelings that charges the text of the novel with certain elements of melodrama.
The stereotypical aspects of the various stages of Jane's life from her state of bondage in Gateshead hall, her sevre oppression in the school where she is sent in the Lowood episode--all have melodramatic colourings. The way the characters are built with contrasting patterns as in Jane and Helen in Lowood have melodramatic aspects. The moment of Helen's death and Jane's presence alongside her and the incarceration within the red room earlier in Gateshead Hall are pertinent examples.
The Gothic experience in Thornfield Hall, especially the violent colour symbolism associated with Bertha, the sequence of Bertha's death and the burning of Thornfield Hall, Rochester's disability are still melodramatic markers in the novel.