1. Preheat broiler.
2. Cut bell peppers in half lengthwise; discard seeds and membranes. Place pepper halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil 15 minutes or until blackened. Place in a zip-top plastic bag; seal. Let stand 10 minutes. Peel and cut bell peppers into thin strips.
3. Combine 1 tablespoon balsamic vinegar and 1 teaspoon honey in a medium bowl, stirring with a whisk. Add onion and thyme; toss well to coat. Let stand for 15 minutes.
4. Combine remaining 2 tablespoons vinegar, remaining 1 teaspoon honey, Dijon mustard, salt, and pepper in a small bowl. Gradually add olive oil, stirring with a whisk. Combine escarole, arugula, bell pepper strips, and onion mixture in a large bowl. Drizzle vinegar mixture over escarole mixture, and toss gently to combine.