What episode did Peter Griffin find out he was a Mexican immigrant?

Answer 1

Technically Yes he is, or was until the Padre de Familia episode.

Mexico and The U.S. have similar laws.

If you're born in Mexico, you're a Mexican citizen regardless of the nationality of your parents, the same as the U.S.

Normally the child would have duel citizenship until they are 18 and then they would choose which one they wanted to be.

Peter never had that opportunity since Thelma says she never filed the naturalization papers for Peter when she returned to the U.S. proving he was born to U.S. citizens so he was a Mexican citizen until he was 42 when he took the U.S. Citizenship Test, granted he failed but made some arrangement with Carter but now he is an American citizen.

Answer 2

Season 6: Episode 6: Padre de Familia