Heat oil in deep oven proof 12-inch skillet or paella pan over medium-high heat. Add thighs and saute, turning once, about 5 minutes. Add wings and saute, turning all pieces once or twice, until light golden, about 12 minutes. Transfer to plate.
Add shrimp to skillet and cook, tossing frequently, 1 minute. Transfer to plate.
Add onion and bell pepper to skillet. Reduce heat to medium and cook, stirring frequently, until slightly softened, about 10 minutes. Stir in sausage, garlic, bay leaf, saffron, and thyme; cook 1 minute. Stir in tomatoes and a pinch each of salt and pepper. Cook, stirring and breaking up tomatoes, about 5 minutes.
Heat oven to 350 degrees.
Add rice to skillet and stir with large fork until grains are translucent, about 5 minutes. Pour broth into quart measure, spoon off fat, and add enough cold water to make 1 quart. Pour diluted broth into skillet and increase heat slightly. Heat to boiling, then gently boil 5 minutes, stirring frequently. Remove from heat.
Tuck chicken and shrimp into rice. Scatter roasted red peppers and peas over top.
Bake uncovered until liquid is absorbed but rice is still moist, about 15 minutes. Add mussels and bake 5 minutes longer.
Remove skillet from oven and cover tightly with foil. Let stand 5 minutes. Scatter olives over paella and serve hot.