Preheat oven to 450 degrees F. For the sauce: In a heavy oven-proof 10-inch saute pan, heat the butter and olive oil over medium heat till the butter sizzles, about 3 min. Add in the onions and mushrooms. Cook, partially covered, till the mushrooms soften slightly, about 5 min. Then add in garlic and cook for 1 minute, remove and put on a plate.
Using the same pan, arrange the swordfish in a single layer.
Stir the wine, capers, anchovies, parsley, mixed herbs, olives and pepper into the sauce. Bring to a boil and simmer uncovered for 2 min, stirring. Pour the sauce over the swordfish, mushroom mixture, olives and bake, uncovered, till fish is barely opaque and slightly springy, 12 to 15 min.
Transfer the swordfish to individual plates and spoon the sauce over. Serve immediately.