HEAT barbecue to medium heat. Cut tops off peppers; remove and discard seeds. Cut peppers into quarters; place in resealable plastic bag. Add mushrooms and 1/4 cup dressing. Seal bag; turn to evenly coat vegetables with dressing. Remove vegetables from bag; discard bag and dressing.
GRILL vegetables 8 to 10 min. or until crisp-tender, turning occasionally.
SLICE mushrooms; place in bowl. Add peppers and remaining 1/4 cup dressing; toss to coat.