Is there a graph theory textbook that covers treewidth thoroughly?
I don't know if the thing you are looking for exists, but here are at least some pointers:
Parameterized Algorithms by Cygan et al (free PDF version) has a chapter dedicated on the topic.  This is slightly algorithms oriented, but contains structural stuff too.
Graph Theory by Diestel has one chapter, (12.  Minors, Trees and WQO) on the subject, about 40 pages.  homepage
Bodlaender has a chapter Treewidth of Graphs in the Encyclopedia of Algorithms.  homepage
Heggernes has a short compendium used for her advanced algorithms class Treewidth, partial $k$-trees, and chordal graphs.
You also have Ton Kloks' book, Treewidth springer, but it's getting rather old.  I have not read this one, so I don't know much about it.