Warum nicht Your mother and your father?
The solution provided by DL (her, her) is wrong. As both Ihre and Ihr are capitalised, at least the second part is always the polite form and hence needs to be translated as ... and your father.
Your solution is correct.
Duolingo, must you tell him/her about that, you should try keep a secret sometimes. ^_^
Can i say: "your mother and your father" or "her mother and her father" as well?