Preheat oven to 350 degrees F. Grease a 9-inch springform pan.
Combine crushed cookies and butter. Press into bottom and slightly up sides of greased pan. Bake at 350 for 10 minutes. Remove from oven.
Beat cream cheese until smooth. Beat in sugar and vanilla and continue beating until fluffy. Reduce mixer speed to low and beat in eggs, one at a time, beating just until mixed.
Spoon out 1 cup of cheesecake batter and combine with melted dark chocolate. Add melted white chocolate to remaining batter in mixing bowl. Stir well.
Pour white chocolate mixture and dark chocolate mixture into pan alternately.
Bake on center rack for 40 minutes or until sides are set. Middle will still appear slightly wiggly. Cool completely on a wire rack. Transfer to refrigerator and chill for at least 4 hours but preferably longer. Texture improves if you chill it overnight.