Pour 4 cups white milk, 1 cup coffee, and 14 oz sweetened condensed milk into a large saucepan; stir to combine.
Add 1 cup milk chocolate chips to the saucepan and stir so the chips are distributed evenly.
Place the saucepan over medium-low heat.
Heat gently, stirring frequently (every 1–2 minutes) to prevent sticking, until the chocolate chips are fully melted and the mixture is smooth and hot. Do not let it come to a rolling boil; gentle steaming and small bubbles at the edge are enough. This typically takes about 10–20 minutes.
Remove the pan from the heat once the mixture is smooth and hot.
Pour into cups and top each serving with mini marshmallows.