Prepare the marinade.
Place the bell peppers in a flat, microwave-safe dish and pour in half of the marinade, making sure to coat the pieces well.
Place the zucchini, squash, eggplant and mushrooms in another microwave-safe dish and pour in the remaining marinade.
Tightly cover both dishes with plastic wrap.
Microwave the peppers for 6 minutes; microwave the other vegetables for 4 minutes. They should still be a little crisp.
Prepare a fire in a barbecue grill. Let the coals burn down to the gray-ash stage.
Working in batches, place a single layer of vegetables (reserving the marinade) on a vegetable-grilling rack on the barbecue, and cook for 2 to 3 minutes, or until you see charred grill marks on the bottom side of the vegetables. Turn and grill the other side for 2 to 3 minutes longer.
Serve the marinade on the side as a dipping sauce.