Dip the berries in the melted semisweet chocolate and drizzle with the melted white baking chips.
Melt the semisweet chocolate chips and 1 teaspoon shortening in a resealable plastic food-storage bag in the microwave on Medium (50%) until chips are softened; squeeze bag until chips are smooth. Snip a corner of the bag, and squeeze for easy drizzling.
Rinse strawberries with cool water just before you are ready to use them, and pat dry with paper towels. If you wash and then refrigerate the strawberries ahead of time, they will turn mushy.