Comparing Beach House's line "we parted our lips and we reached from inside" to Mazzy Star's "I want to hold the hand inside you"
Both these lines speak about knowing a person to the core. It's about getting to know someone's soul. If for example two people are physically attracted to each other and already understand each other's personalities what they would desire next is to know each others souls. Soul? The part of us that tells us where to look, what to think, what to say. That ghostly thing within us that activates our thoughts and body.
Both these lines speak about knowing a person inside out to form a spiritual bond. I like the way that both songs paint it as if we have invisible hands that are able to travel through the body and grasp someone else's soul. It's all about connecting with someone as if two were one. Perhaps, Beach House's line has more to do with speaking sincerely from the heart so as to "reach" into each others souls when communicating. Or "parted our lips" could also be about kissing but I like to think of it as speaking. Do with it what you may. Is it a bit of a cheesy concept? Yes; well maybe not if you're in love OR feeling like a romantic.
Beach House "lover of mine"
Beach House - Lover Of Mine by musicmule
Mazzy Star "fade into you"
Mazzy Star / Fade Into You by ShornStarMan