Sprinkle fillets with tarragon, salt, and pepper; dredge lightly in flour.
Cook fish in butter and hot oil in a large skillet over medium heat 7 to 8 minutes on each side or until fish flakes easily when tested with a fork. Remove fish from skillet, and place on a serving platter. Set aside, and keep warm.
Drain drippings from skillet, reserving 2 tablespoons in skillet. Add Madeira; cook over medium heat 4 minutes or until reduced to 2 tablespoons, deglazing skillet by scraping particles that cling to pan. Stir in lemon juice and capers; cook until thoroughly heated. Pour sauce over fish, and sprinkle with parsley.