Edit: The list below fits not that good to the requirements you describe, but the texts there are what I found helpfull. If you can read German books, I would recommend W. Greiner's "Theoretische Physik", which explains basically all the needed mathematics. Usefull too may be J. Baez' "Gauge Fields, Knots and Gravity", which contains a "rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations".
I found Novikov, Shifman, Vainshtein, Zarkhavov's "ABC of Instantons" very good and helpfull to enter the 'physicist's mindspace'.
And then, I found F. C.'s recommendation to Nahm's very fascinating "Conformal Field Theory and Torsion Elements of the Bloch Group" very good, e.g. Nahm writes "readable for mathematicians", "much of this article is aimed at mathematicians who want to see quantum field theory in an understandable language .... all computations should be easily reproducible by the reader". Nahm's issue is a strange connection between some quantum field theories and algebraic K-theory and he hopes, his article could stimulate mathematicians to become interested in these exciting topic. A forthcoming article by Zagier on "quantum modular forms" may relate to that too.
Very interesting too is Nahm's article on the very strange and puzzling history of quantum field theory and string theory, which makes mathematicians so much headaches.
Connes/Marcolli's book"Noncommutative Geometry, Quantum Fields and Motives" contains a very readable introduction in quantum field theory, renormalization etc., Marcolli's "Feynman motives" a chapter "Perturbative Quantum Field Theory and Feynman Diagrams".
Rabin hold a very readable "Introduction to Quantum Field Theory for Mathematicians" in this conference.