Line a 10x13-inch baking dish with parchment paper.
Mix sweetened condensed milk, chocolate chips, and unsweetened chocolate together in a microwave-safe bowl. Cook in the microwave on high for 30 seconds; stir. Continue cooking in microwave, stirring every 30 seconds, until chocolate is melted and smooth, 1 to 2 minutes. Stir.
Cook melted chocolate mixture in the microwave on high, stirring every 2 minutes, for 6 minutes. Stir vanilla extract and salt into fudge. Beat fudge with an electric mixer for 2 minutes; pour into the prepared baking dish.