Heathcliff, like Rochester and Higgins, is also changeable and moody. But he's darkly so. He's always sinister, even when acting kind. Most of the time, his quick changes in mood are when he figures out how he can manipulate the people around him to suit his plans for revenge and ruining everyone's life. Happy person. That pessimism links him closely to Rochester, who broods over his past, then broods over losing his only hope in Jane. But Rochester only broods, Heathcliff acts with vehemence.
Though it's odd: I think of Heathcliff as having a naturally good center hidden somewhere inside of all his evil and Rochester as having a naturally hard and dark center inside his attempts to overshadow it. Which in the end, he does manage to do, thanks to Jane for "showing him the light." Going back to that pity I have for Heathcliff, I don't think he ever really wanted to do wrong. But he had no one. He had an adopted family that didn't like him much. He had a friend that he loved who was forsaking him for a passing (and rich) fancy of hers. It killed the good in him. It makes me wonder what Heathcliff would've been like if he had chosen differently. He threw himself so entirely into his evil purpose that I'd like to see that force put into a good purpose.
I said that the good in him was killed, but it wasn't entirely taken away, all the same. This is why I see him with a good center: even in all his darkness, he still remembers Cathy so tenderly. He tries to gouge out his heart, but it's still there. Which is similar to how Rochester simply despairs without Jane, but still loves her and is able to continue on with her so easily when she does come back.