No, I think the love between them is abnormal.

Catherine and Heathcliff's passion for one another seems to be the center of Wuthering Heights, given that it is stronger and more lasting than any other emotion displayed in the novel, and that it is the source of most of the major conflicts that structure the novel's plot. Catherine and Heathcliff's love is rooted in their childhood and is marked by the refusal to change. In choosing to marry Edgar, Catherine seeks a more genteel life, but she refuses to adapt to her role as wife, either by sacrificing Heathcliff or embracing Edgar. Moreover, Catherine and Heathcliff's love is based on their shared perception that they are identical. Catherine declares, famously, “I am Heathcliff,” while Heathcliff, upon Catherine's death, wails that he cannot live without his “soul”, meaning Catherine. Their love denies difference, and is strangely asexual.