OK...think about what a doubly linked list needs to have:
Node 1 2 3
Prev 0 <-1 <-2
Next 2-> 3-> 0
So when you try to insert a new node between 1 and 2, you have to affect 1's Next node, and 2's previous:
Node 1 x 2 3
Prev 0 <-1 <-x <-2
Next x-> 2-> 3-> 0
So:
node.next.prev:=newNode
Is inserting the "x" reference in the "prev" link of the next node: the "x" in the "Prev" of "2" in my example.
Try it with pen and paper: it'll make sense!