Line a baking sheet with waxed paper.

Melt chocolate chips in top of a double boiler over simmering water, stirring frequently and scraping down the sides with a rubber spatula to avoid scorching, 3 to 5 minutes.

Melt white chocolate chips in top of a separate double boiler over simmering water, stirring frequently and scraping down the sides with a rubber spatula to avoid scorching, 3 to 5 minutes. Stir in vegetable oil and peppermint extract.

Pour chocolate onto lined baking sheet; spread with spatula. Drizzle white chocolate over chocolate; swirl with a fork.

Refrigerate until bark is hardened, about 1 hour.