In a medium saucepan over low heat, combine milk chocolate chips, unsweetened chocolate and butter. Heat until melted and smooth, stirring occasionally. Remove from heat and stir in condensed milk, peppermint extract and vanilla extract.
Beat with an electric mixer at a low speed for 1 minute, then at a high speed for 1 minute. Chill mixture for 15 minutes, beating by hand every 5 minutes. Beat again with electric mixer two minutes more. Pour into prepared pan and chill until firm. Cut into 1/2 inch squares.