Cut bell peppers in half lengthwise, discarding seeds and membranes. Place pepper halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil for 10 minutes or until blackened. Place in a zip-top plastic bag; seal. Let stand 20 minutes. Peel and set aside.
Cut off artichoke stems, and remove bottom leaves. Trim about 1 inch from tops of artichokes. Bring water, lemon slices, and bay leaf to a boil in a large Dutch oven. Add artichokes; cover, reduce heat, and simmer 25 minutes or until a leaf near the center of each artichoke pulls out easily. Drain well; discard lemon and bay leaf. Set aside.
Combine bell peppers, oil, mustard, and vinegar in a blender; process until smooth. Combine bell pepper mixture, fines herbes, and black pepper. Spoon 2/3 cup into a serving bowl; sprinkle with feta and capers. Serve with artichokes. Cover and chill remaining dip.