Preheat oven to 350°F (180°C).
Pour milk, cream and coffee into bowl; whisk together.
Add rum and beat with electric beater.
Add sugar and continue beating to incorporate.
Lightly beat eggs with fork.
Pour into bowl containing custard mixture and whisk well until incorporated.
Place 6 individual custard dishes in roasting pan and pour in 1 inch (2.5 cm) hot water.
Fill custard dishes with mixture and bake 40 minutes.