What kind of relationship do Nora and Helmer have? How would you analyze such a relationship in the context of the story?

Nora herself describes her relationship with Torvald by saying to Torvald that she is "no wife" for him; she is only his "doll" (Act 3).
One of the reasons that Nora contends that she is not a wife to Torvald is the fact that her husband does not appreciate how she has saved his life; instead, he scolds his wife for her crime of forgery and the public embarrassment it has brought him. In Act 3, when she talks with her husband seriously after the party has ended and he has read Krogstad's letter, he calls Nora a "criminal" and a "hypocrite," and he doesn't have any appreciation for her sacrifices to repay the loan.
Nora's forgery is the leading cause of Torvald's ire and her desire to leave him. Because of his lack of appreciation for her saving his life, she also resents his treating her as though she were a child, such as when he forbade her to eat macaroons or scolded her for being a spendthrift. But, whenever he was pleased with her as his "doll," who gave him pleasure, he would call her pet names. She tells him, "You never loved me––...You only thought it was fun to be in love with me" (Act 3). Further, Nora objects to the law that prohibited her from trying to "spare her dying old father or save her husband's life!" (Act 3).
Finally, Nora tells Torvald that she must learn about the society in which she lives. "I have to make up my mind who is right, society or I." (Act 3) Then, she leaves her home and children, saying goodbye to her husband.