In a small bowl, stir together softened butter, olive oil, garlic, desired herb, salt, and black pepper. Set aside. In a large bowl, toss together potatoes, onion, sweet pepper, and mushrooms.
Fold a 44x18-inch piece of heavy foil in half to make an 22 x 18-inch rectangle. Place the vegetables in center of foil. Drizzle butter mixture over vegetables. Bring up opposite ends of foil and seal with a double fold. Fold remaining edges together to completely enclose vegetables, leaving space for steam to build.
For a charcoal grill, arrange medium-hot coals around edge of grill. Test for medium heat above the center of the grill. Place packet on grill rack over center of grill (not directly over coals). Cover and grill for 35 to 45 minutes or till potatoes are tender. (For a gas grill, preheat grill on high for 10 to 15 minutes. Reduce heat to medium. Adjust for indirect cooking. Grill as above.)
Remove packet from grill. Carefully open packet. Serve immediately. Makes 5 or 6 side-dish servings.