Bertha is both a foil and a mirror for Jane Eyre. She is the foil or opposite of Jane in terms of their behavior, while both are living at Thornfield. While Jane is quiet, demure, and self-controlled, Bertha is loud, aggressive, and out of control. If Jane represents sanity and good order, Bertha represents madness and chaos. The supportive and helpful Jane is the "good" wife Rochester craves, while the "mad" Bertha is the "bad," unsupportive wife he is saddled with.
Yet Jane and Bertha also share striking similarities. Bertha's red or bloodshot eyes bring us back to the red-room in which the child Jane was imprisoned. Jane was locked there after an incidence of "madness" when she lost control and attacked John Reed, her constant tormentor. This is not so different from Bertha's being locked away for aggressive behavior against a patriarchal male who acts as her oppressor. If Bertha shouts in her captivity, so did the young Jane in the red-room.
Point of view makes all the difference in how we see each character. We are told the story of Jane's childhood "madness" from her point of view, and so we sympathize with her as the oppressed underdog having a justified rebellion against being enslaved by John's tyrannies. In the case of Bertha, she is never allowed to tell her side of the story. We receive it as filtered through Rochester and Jane, who, like Mrs. Reed, prefer simply to label a "problem" person an insane other who has to be locked away. Neither perceives Bertha as a human being who might respond and improve should someone try to understand her perspective.
Both Jane and Bertha suffer from intense anger over how they are treated in patriarchal domestic situations: Jane finds ways out, while Bertha does not, except through death.