1. 彼の家族はとてもフレンドリーで、私を快く(こころよく)迎えてくれた。
2. 彼はクラスメートに親切だ。(もしくは、優しい)
When I use the word kind, I use it in the way you described. Like, she is やさしい, she kind-hearted.
And when I use the word friendly, I mean the same thing you said too. Easy to be friends with, so it's normally used for someone who you meet for the first time. (And we say フレンドリー in Japanese too.)
As far as I think, friendly people are not always kind and kind people are not always friendly, so these 2 words don't have the same meaning in my opinon.
Hope this is helpful.