When Sonia G writes "...when speaking in Italian, you should never leave out the definite (or indefinite) article", I'm assuming she means in this particular case, that is, 'la mia famiglia'.
With many of the terms for relatives in the singular, the article is left out if the possessive adjective comes before the noun, e.g. 'mia sorella'. The plural form, however, takes the article: 'le mie sorelle'. Note also that if the possessive adjective comes AFTER the noun, the article is used, e.g., 'la sorella mia'. And, if the noun is qualified with an additional adjective, the article is also used, e.g., 'la mia vecchia madre'.