Coat a 9-inch springform pan with cooking spray; wrap a large piece of heavy-duty aluminum foil around bottom and up sides of springform pan. Sprinkle cookie crumbs in bottom of pan; set aside.
Beat Neufchâtel cheese and sour cream at medium speed of an electric mixer until creamy. Gradually add sugar, beating well. Add eggs, one at a time, beating at low speed after each addition. Stir in almond and vanilla extracts.
Spoon 2 cups of batter into a medium bowl; add cocoa, stirring well. Pour half of chocolate batter into prepared pan. Spoon plain batter over chocolate batter. Drop remaining chocolate batter, one tablespoon at a time, over plain batter. Swirl with a knife to create a marbled effect.
Place prepared springform pan in a shallow pan. Add hot water to pan to depth of 1 inch. Bake at 325° for 55 minutes (center will be soft but will firm when chilled). Turn off oven, and partially open oven door; leave cheesecake in oven 1 hour. Remove from oven, and let cool to room temperature on a wire rack. Cover and chill 8 hours.