My wife heard this a couple of days ago on television.

Problem:
The definite article “the” is incorrect in this phrase.

Explanation:
The word “both” is an adjective that means two together (e.g., “I saw both suspects.”), a pronoun that means the one as well as the other (e.g., “Both of them were flying to Paris.”, or a conjunction that means alike or equally (e.g., “Jim is both tall and handsome.”).

It’s clear, then, that the word “both” was used as a pronoun in the phrase that my wife heard.

Pronouns do not take articles in front of them, so “the both” is always incorrect.

Beyond that, one can see that “the” (or “a”) should never precede “both” in a sentence.

For fun, I searched Google for “the both” (with quotation marks) and got about 2,130,000 matches. Some of those matches were for grammatically correct forms such as “the Both Sides Now album”; most, though, were incorrect.

I believe that this common English blunder sometimes indicates hypercorrection: if “both” is good, then “the both” must be better. Wrong!

Solution:
“… for both of us.”