What is Heathcliff's relationship with Isabella?

Answer 1

Heathcliff married Isabella to get revenge on Edgar Linton. Isabella thinks Heathcliff's cold actions when he returns to Wuthering Heights after he's been gone for three years are hiding his gentle side, and thinks her love will bring that part out in him. Heathcliff hates Isabella though, and thinks she's a fool for marrying him, it's implied that he beats her even. Isabella has Heathcliff's child, though after marrying him she realises he is violent and cruel.

Answer 2

She is his wife.

However, I assume this is possibly an English lit question, therefore the answer is far more involved and must include the complex nature of the relationship and it's origins.

Suggest you read the book.