We investigate the classical and quantum mechanics of diatomic molecules in combined electrostatic and pulsed laser fields. The integrable case of collinear static and linearly polarized laser fields exhibits both classical and quantum monodromy, and energy-momentum diagrams are presented for several physically relevant field combinations. Although the tilted field problem is nonintegrable, a quantum :root lattice for eigenstates retains much of the structure of the integrable limit and is organized by classical periodic orbits. The regular structure of the quantum lattice in the integrable limit is disrupted in an energy range associated with the onset of chaotic classical motion. (C) 2004 Elsevier B.V. All rights reserved.