Heathcliff is first discovered by the Earnshaw family on the streets of Liverpool, where they decide to take him in and raise him as their own. In this most external of respects, Catherine is his foster sister, and she initially resents him along with her brother. However, as their childhoods progress, the relationship and attachment becomes far more complicated, venturing into the romantic and bordering on the obsessive.
As they grow, the enter a forbidden love that they seem to believe is ordained by fate. They claim that their souls are the same, with Catherine delivering the famous line, "I am Heathcliff." Though she truly loves Heathcliff, she knows that match would degrade her, and Heathcliff is only aware of her feelings in regard to the latter fact. This lack of knowledge of her reciprocal feelings lead to Heathcliff's bitterness and vindictive actions.
When Catherine dies, Heathcliff becomes more tormented than ever. He claims he is being haunted by her ghost and even goes as far as to dig up her corpse. Eventually, death is his only respite from this pain.