In a medium bowl combine red wine vinegar, lemon juice, rice vinegar, brown sugar, basil, oregano, mustard, garlic, salt, and pepper. Add salad oil and olive oil in a thin, steady stream, whisking constantly until combined.
Use immediately or cover and chill for up to 3 days before using. If chilled, let stand at room temperature for 30 minutes; whisk before using. Makes about 2-2/3 cups.