Snap off tough ends of asparagus. Place asparagus, onion, bell pepper, squash, and zucchini in a large heavy- duty zip-top plastic bag.
Combine balsamic vinegar and next 8 ingredients; pour over vegetables in plastic bag. Seal bag, and shake gently to coat vegetables. Marinate 30 minutes, turning bag occasionally.
Remove vegetables, discarding marinade. Place vegetables in a grill basket. Grill, uncovered, over medium- high heat (350° to 400°) 22 minutes or until slightly charred, turning often.