My Wife and I vs My Wife and Me
The correct phrase is "My wife and I."
The rule is that when you use a personal pronoun (like I or me) in a compound subject or object (with another person, like my wife), you should determine which pronoun is correct by temporarily removing the other person.
Here's how to check:
If it's the subject of the sentence:
Incorrect: My wife and me went to the store. (Would you say: Me went to the store?)
Correct: My wife and I went to the store. (Would you say: I went to the store?) → My wife and I is correct.
If it's the object of the verb or a preposition:
Incorrect: The gift was for my wife and I. (Would you say: The gift was for I?)
Correct: The gift was for my wife and me. (Would you say: The gift was for me?) → My wife and me is correct.
So, while "My wife and I" is correct when used as the subject, "My wife and me" is correct when used as the object. Since you only provided the phrase without a sentence, the phrase that is grammatically correct as a subject (the most common context for this kind of question) is "My wife and I."