Combine 1/2 cup semisweet chocolate chips and 1/2 cup milk chocolate chips in a double boiler over simmering water; stir frequently, scraping down the sides with a rubber spatula to avoid scorching, until melted, 3 to 5 minutes. Remove from heat; stir in remaining semisweet and milk chocolate chips.
Line a baking sheet with waxed paper.
Holding strawberries by their stems, swirl through melted chocolate until all sides are evenly coated. Arrange dipped strawberries on the waxed paper.
Chill strawberries until chocolate coating sets, about 2 hours.