Mixed Lemony Rice: In large saucepan, cook rice with salt according to package directions. Stir in chives and lemon juice.
Meanwhile, arrange mushrooms, stemside up, on lightly greased rimmed baking sheet. Bake in 450 F (230 C) oven until browned and tender, about 15 minutes. Using tongs, tip mushrooms to discard any liquid; pat dry with paper towels. Sprinkle with salt and pepper.
Meanwhile, in skillet, heat oil over medium heat; cook shallots, garlic and thyme until garlic is fragrant, 1 minute. Add spinach; cook, stirring occasionally, until wilted, 3 minutes. Add raisins; cook, stirring, until no liquid remains, about 2 minutes. Remove from heat. Stir in feta cheese. Spoon into mushrooms. Sprinkle with mozzarella cheese and almonds. Bake until cheese is melted and almonds are browned.
Lemon Yogurt Sauce: In bowl, stir together yogurt, mint and lemon zest. Serve with stuffed mushrooms and rice.