Peel the squash and sweet potatoes. Slice the neck of the squash and the sweet potato into 1/4 rounds.
In a buttered 13x9 baking dish lay 1/2 of the squash followed by 1/4 of the thyme and cheese. Do the same for 1/2 the sweet potato. Repeat using the rest of the ingredients.
Bake in a 375F oven covered in foil for 30 minutes. Remove the foil and bake another 20 minutes.