In a large bowl, stir together the pudding mix with the milk and coffee until very thick.
In another large bowl, beat the heavy cream with the sugar and vanilla using an electric hand mixer until soft peaks form. Reserve 1/4 cup for garnish.
Stir one-third of the whipped cream into the pudding to lighten it. Fold the remaining whipped cream gently into the pudding. Spoon into dessert glasses and refrigerate until ready to serve. Mousse can be made ahead up to 4 hours in advance. When ready to serve, top each with a small dollop of the reserved whipped cream and sprinkle with the chocolate chips.