Combine zucchini, summer squash, bell peppers, onion and vinaigrette in a 1-gallon recloseable food storage bag; seal. Toss to coat; let stand 30 minutes. Brush bread with olive oil.
In food processor or blender, combine cheese, olives and basil; process until pureed. Set aside.
Prepare grill to medium heat. Remove vegetables from vinaigrette; place on grill. Grill until tender, turning occasionally (about 10 minutes). Grill bread until golden brown (about 3-5 minutes).
Spread cheese mixture over bottom of bread. Top with spinach; layer with vegetables. Cover with top of bread and cut into 6 sandwiches.