This structure in greek is called "Υποθετικός Λόγος (Hypothetical Speech)". It is the same as in English.
The translation is absolutely right, with only one mistake.
Let's see the sentence again:
"If Andreas died tomorrow, you and me would have to pay for this house."
Andreas is the subject in the first sentence. So, the translation will be like
"Αν ο Ανδρέας πέθαινε αύριο, εσύ και εγώ θα έπρεπε να πληρώσουμε για αυτό το σπίτι."
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.