In a medium bowl, cream the butter, white sugar and brown sugar together with a wooden spoon. Add eggs and vanilla, mix well. Sift together the flour, bicarb soda and salt, stir into the creamed mixture. Finally stir in the dark chocolate chips and the white chocolate bits, if the batter is too stiff, you may need to use your hands.
Drop biscuits by heaping spoonfuls onto unprepared baking trays. Bake for 7 to 10 minutes in the preheated oven. I always like to take my biscuits out of the oven when they are light brown and not yet set. It creates a softer biscuit. Allow biscuits to cool for a few minutes on the baking tray before removing to cool on wire racks.