Very good question, as it penetrates to the very heart of the crux of this fascinating novel. Heathcliff is what is called a Byronic hero, a term used to describe a Romantic hero who was brooding, solitary, and isolated from society. Your answer to the question entirely depends on how you read the novel - Heathcliff can either be viewed as an upstart (indeed Nelly Dean describes him as a "cuckoo") who ruins relations between the Lintons and the Earnshaws in every way possible, or a frustrated, maltreated orphan who is driven to commit heinous acts because of his intense but thwarted love for Catherine.
Another question you need to consider about Heathcliff is how he is presented. For in the novel at times he appears to be described as a monster, at others as a man just like the rest of us. Compare these two quotes, for example:
"Poor wretch!" I thought; "you have a heart and nerves the same as your brother men!"
He dashed his head against the knotted trunk; and, lifting up his eyes, howeled, not like a man, but like a savage beast getting goaded to death with knives and spears.
Both quotes come from Chapter 16 after Catherine's death and capture the dilemma - is Heathcliff a man or a monster? So to summarise, your answer will depend very much on how you view Heathcliff.
This really depends on the reader and which part of the novel they felt where more important than the other. For me I would have to say Heathcliff feed more into being the antagonist more than a protagonist. Heathcliff is responsible for making Isabella escape by forcing her into marriage with fake stories of love. He also is to blame for forcing Catherine, Catherine's daughter, into marrying his because he wants to take of the Grange. Heathcliff is hostile to everyone even Catherine his reason to even exacting revenge. However I also understand where it comes from since society shunned him because he held no education, status, or wealth. This is why some may regard him as a hero because he climb the ranks of society after be shunned so brutality.