Line an 8-inch square baking dish with foil, leaving a 2-inch overhang on two sides; lightly coat the foil with cooking spray. Combine the condensed milk, semisweet and milk chocolate chips, butter, espresso powder and salt in a medium saucepan. Place over medium heat and cook, stirring and scraping the bottom of the pan frequently with a rubber spatula, until the chocolate is completely melted, about 5 minutes.
Combine the dulce de leche and white chocolate chips in a small microwave-safe bowl. Microwave in 15-second intervals, stirring, until melted, about 30 seconds.
Spread the semisweet chocolate mixture in the prepared baking dish. Immediately drizzle the dulce de leche mixture on top. Drag a butter knife through the dulce de leche mixture to make a marbled pattern on top. Let cool completely at room temperature, about 1 hour. Cover with plastic wrap and refrigerate until firm, at least 2 hours or overnight.
Lift the fudge out of the baking dish and peel off the foil. Cut into 1-inch squares with a sharp knife.