For me, there's a subtle difference between the two:
zwischen den Zeilen lesen, means that you accept what is there but realize there is more than meets the eye, i.e. you take in what is obviously seen but then search further.
hinter die Fassade schauen means that you realize right away that what you see with your eyes is rather fake and you know that you have to look further.
I can't prove it with a rule, but it's my language feeling speaking (I'm a native German).