The Rama (the rishon), in Kesubos 40a, writes that even when a parent says that he is not interested in the action, the assei nevertheless applies. Rabbi Akiva Eiger (Yoreh De’ah 240:19) quotes from the Radvaz 1:524 (that derives from the Rama) that even though the Gemara in Kiddushin 32b states that a father may forgo his honor, this only provides for no punishment for not having shown honor and respect. But if a child nonetheless shows honor and respect, it is a kiyum mitzvah.
The Chayei Adam, in hilchos kibud av v’eim (67:1), says that the mitzvah of kibud av v’eim is the repayment of a debt that one owes to one’s parents for all the good they have shown him. One who does not show his parents respect and honor is considered a rasha, for the pasuk states that one who does not repay his debt is a rasha. This implies that the mitzvah of kibud av v’eim is a mitzvah bein adam lachaveiro.