No, Jane does not think that she is inferior to Mr. Rochester. Jane is an educated woman who is subjected to a caste system of society, but that does not make her less capable in any way to stand next to him or to have an educated conversation with him. The 19th century society in which they lived may have seen her as an inferior to Mr. Rochester, but her own view was completely different. She best explains her position before Mr. Rochester in chapter seventeen:
I at once called my sensations to order; and it was wonderful how I got over the temporary blunder—how I cleared up the mistake of supposing Mr. Rochester's movements a matter in which I had any cause to take a vital interest. Not that I humbled myself by a slavish notion of inferiority: on the contrary, I just said, “You have nothing to do with the master of Thornfield, further than to receive the salary he gives you for teaching his protégé, and to be grateful for such respectful and kind treatment as, if you do your duty, you have a right to expect at his hands. Be sure that is the only tie he seriously acknowledges between you and him: so don't make him the object of your fine feelings, your raptures, agonies, and so forth. He is not of your order: keep to your caste, and be too self-respecting to lavish the love of the whole heart, soul, and strength, where such a gift is not wanted and would be despised”(118).
Clearly, the above passage shows Jane attempting to pull her emotions and her profession into check as she realigns her attitude and perspective. She explicitly says that she does not put her self down and out of his way because of any sense of inferiority. In fact, she uses the caste system to keep her emotions in check and to remember that she is an employee at the house, not the mistress. This is all during a time when Rochester is manipulating their relationship by trying to prove to her that she hasn't ever really loved before; and, too, that to love is to be jealous and to pine away for someone. In this sense, Mr. Rochester is beneath Jane because he stoops to manipulation in order to see if she will fall for him.