Hilchos Lashon Hara chapter 8, section 14

Accepting lashon hara is forbidden the same way whether he hears it from strangers or from his father and mother and his household.

More than that, it is written in Tanna Devei Eliyahu, chapter 21: if he sees his father and mother speaking words they should not, like lashon hara, he is not only warned not to accept the lashon hara, he also must correct them so that they stop. If he stays silent, both he and they are punished severely.

It is written in Masechet Shabbos (54b) that someone who could protest against the people of his household and does not, is punished for them in the World to Come. So a person should always be used to correcting the people of his household about such things, but only with gentle words. He should explain to them how great the punishment for this is, and how great the reward is for someone who is careful about it.

Above all, he should be careful himself that the people of his household never hear him say bad things about others. If he himself breaks the prohibition of lashon hara, then besides the sin itself, he will have no ground to correct them later. Usually, the way a household behaves is shaped by the head of the house. So he must be very careful about this himself.