Measure 5 tablespoons of sweetened condensed milk into a microwave-safe bowl and fold in the white chocolate chips. The chips should have a coating of milk, though the mixture will still look chunky.
Empty the remaining condensed milk into a separate microwave-safe bowl containing the dark chocolate chips. Keep the two mixtures separate to preserve their different proportions and colors.
Fit foil or parchment into your square pan with enough overhang to grip later, then generously coat the lining with butter or shortening. A well-greased lining helps release the firm block without tearing its edges.
Heat the dark chocolate mixture for 30 seconds, stir, heat for another 15 seconds, then beat vigorously until smooth before scraping it into the pan and leveling the surface. The chips may retain their outlines after heating, but stirring distributes the warmth and turns the mixture glossy.
Give the white chocolate mixture 30 seconds in the microwave, stir until smooth, then distribute small spoonfuls over the dark layer and gently connect them into a thin covering. Light strokes keep the pale topping distinct instead of pulling dark chocolate through it.
Scatter the marshmallows over the white chocolate immediately and press them lightly into place. The surface should still feel tacky enough to hold the topping without swallowing it.
Place the pan in the refrigerator for at least 6 hours before attempting to cut the fudge. The center needs to become firm enough to hold its shape, not merely develop a set surface.
Lift the chilled block onto a cutting board using the lining overhang, then carefully peel away all the foil or parchment. The bottom and sides should release as a solid slab.
Slice the block into bite-sized pieces with a sharp knife and transfer them for serving. Each piece should show a dark bottom, a pale top, and an attached marshmallow coating.