Soften the ice cream in the refrigerator until it can be whipped with an electric beater.
Melt the semisweet chocolate in a double boiler over warm water, stirring occasionally.
Allow to cool slightly.
Dissolve the instant coffee in the rum.
Transfer the ice cream to a large mixing bowl.
Whip the ice cream on low, slowly pour the cooled melted chocolate into the ice cream, and continue beating until chocolate is completely incorporated.
Gradually pour in coffee-rum mixture, and continue beating.
Transfer ice cream to a covered freezer container.
Freeze for several hours before serving.
If ice cream becomes solid, allow to soften slightly in refrigerator before serving.