Heat broiler, with rack in top position. Combine yogurt, mustard, capers, and 1 teaspoon oil. Season with salt and pepper.
Pat fillets dry with paper towels. Coat one side of fillets with 1 teaspoon oil and arrange, oil side down, on sheet. Spread yogurt mixture on fillets. Broil until fish is opaque throughout and yogurt mixture is bubbling and browned in spots, about 5 minutes. Toss greens with remaining 2 teaspoons oil, season with salt and pepper. Serve fillets with greens and lemon wedges.