Line a sheet pan with a piece of parchment or waxed paper.
Put the candy or broken candy canes into a plastic bag and crush with a rolling pin or heavy skillet until you have small pieces.
Place the bittersweet chocolate chips in a microwave safe bowl and heat on high until most of the chips are melted, about 2 minutes. Alternatively you can put the chips in a heatproof bowl over a pan of barely simmering water (making sure the bottom of the bowl does not touch the water) and melt the chocolate. Stir until all the chips are melted and the chocolate is smooth and glossy. Pour onto the paper and spread into an even layer with a spatula about an eighth or a quarter inch thick.
Put the white chocolate chips in a microwave safe bowl and heat on high until they start to melt, about 2 minutes. Alternatively you can put the chips in a heatproof bowl over a pan of barely simmering water (making sure the bottom of the bowl does not touch the water) and melt the chocolate. Stir until smooth. Drop spoonfuls of the white chocolate here and there with a spoon onto the semisweet chocolate. With a knife or back of a spoon swirl the white chocolate into the bittersweet. Sprinkle the candy pieces over the chocolates. Let cool. Place in the refrigerator until hard, about 30 minutes. Cut or break into irregular sized and shaped pieces.