Place 2 trout fillets in a deep dish and sprinkle with half the chives and half the dill. Place the other 2 fillets on top, and sprinkle the rest of the dill and chives.
Mix the oil and lemon juice in a glass jar and add the mustard. Pour the sauce over the trout fillets, which should be half-covered by it. Cover the plate with plastic wrap and refrigerate for 2 to 3 hours, or overnight.
Serve at room temperature with thin slices of toasted bread.