Lightly grease 13- x 9-inch baking dish. Spread 2/3 cup of the Alfredo sauce in bottom of pan; set aside. Reserve 2 tbsp of the parsley for garnish.
In large saucepan, melt butter over medium-high heat; cook onion, red pepper, mushrooms and thyme for 4 or 5 minutes or until tender. Stir in remaining Alfredo sauce; bring to boil. Reduce heat to simmer; add crab and spinach. Simmer for 5 minutes and remove from heat. Stir in remaining parsley and chives.
Place 3 lasagna noodles in bottom of prepared baking dish. Top with one-quarter of the crab mixture and sprinkle one-quarter of the cheese over top. Repeat layers three times.
Cover and bake in 350°F oven for about 45 minutes or until golden around edges. Uncover and bake for about 15 minutes or until cheese is golden brown. Sprinkle with reserved parsley; let stand for 10 minutes before serving.