Silly sounding question since your name is Sesami, but we have our little Rei (boy --kinda a girls name in Japanese isn't it) watch in both langages (not the the same time --unless I can't figure out which the kanji for the right button I need to push).
My wife likes to use both languages in the same sentence. She thinks it's 'kawaii', and does it as a habit. I do too especially with 'ne'.
We really need to stop that I think.
Anyway, did you see MacDonalds (here in Tokyo I believe) started English lessons for little ones to get them hooked early. If that's the only way for your child to learn it, maybe being monolingual and having healthy eating habits is better. Just kidding...