In a heavy saucepan over medium high heat, combine the butter, milk, and sugar. Bring to a boil, stirring constantly. Once boiling, cook, without stirring, for 2 minutes. Remove from the heat.
Stir in the marshmallows until melted. Next, add in both chocolates and stir until melted. Add in the vanilla and mix.
Pour the fudge mixture into the prepared dish. Let cool for 1 hour.
After an hour, gently score the fudge and refrigerate for at least 4 hours before cutting.