"Who are your parents?"
Translation:Qui sont tes parents ?
"Qui est-ce que" is a direct object. "Qui est-ce qui" is what you want to use if you're looking for a subject pronoun.
Qui est-ce qui veut aller. - WHO wants to go. Subject
Qui est-ce que tu connais. - WHOM do you know. Direct object of the verb "connais".
Check out the book, "The Ultimate French Review and Practice". It contains an entire section about interrogative pronouns, which I used to find very confusing. Hope that helps!
Then it would have to be 'Tes parents. Lesquels sont-ils?' Quel is an adjective and always needs a noun, lequel is a pronoun and can thus be used as the predicate in a sentence with to be. You could have said 'Quels parents sont-ils?, but that means 'Which parents are they,' and this sounds weird. If you want to say 'Whose parents are they,' you'd say 'De qui sont-ils les parents,' though I'm not sure about that, would have to ask French friend...