1. Prepare gas grill for cooking over direct high heat. While grill heats, cut peppers lengthwise into quarters, discarding stems and seeds. Trim ends so that quarters lie flat.
2. Sprinkle tuna all over with 1 teaspoon salt and 1/2 teaspoon pepper. Cook tuna and peppers on lightly oiled grill rack, turning over once, until tuna is pink only in center and peppers are just tender, 4 to 6 minutes total (peppers may take longer than tuna).
3. While tuna cooks, whisk together lemon juice, mustard, and remaining 1/4 teaspoon salt and 1/2 teaspoon pepper in a small bowl, then add oil in a slow stream, whisking until emulsified. Whisk in capers and parsley.
4. Transfer tuna and peppers as cooked to a serving plate.
5. Serve tuna topped with peppers and caper vinaigrette.

Serves 4.