Unfurtully ModelOne3137735 the answer is yes.
All three players has to be gold
But live has a feature in some games can your friend can like
If the intention of your friend is only olay whiout gain archivement and etc...
Much games gives the option to player like in invited mode in that mode use´s only your gold signature and other player can play the game like you invited then in your console.
Good, has only two problems the "invited" player don´t gain archiment points and nofing for his profile (to chose that option see in the part you chose gmae tag of second player has the "Last" option invite).
The other problem is not all games has that option (= in diablo 3 i don´t know) some games like Halo series has that option, other like Ultimate Marvel Vs Capcom 3 has not.
Again in the part of second player starts look if has the option invite or guess if have your friend can play whif you and other internet player´s
For the third time he will gain nofing, zero of game score.
I hope if i helped you and forgive my bad english, it´s self learnerd.