Does this sound okay?

Yes, and repetitive.

In all seriousness, when you say "beside" you are implying the "parallel" bit. Also, it's rather stiff and, well, mathematical.

As a suggestion, depending on the intimacy of the scene, how about "her body aligned with his"?

As a reader, I would be more interested in knowing if her body was touching his or how far apart their bodies were. I agree with SLCBOSTON that "parallel" is too mathematical.

I think "she stretched out beside him" says all you need. No need to overwork it. What happens after that is probably far more interesting.

Sounds like an erotic moment coming up. For proofing such things talk them out so you don't end up with one person having three hands on another on the head, a breast and a thigh--unless they're Martians :}