hai provato a fare + volte la stessa cosa?
codice:

messageBodyPart1 = new MimeBodyPart(); 
DataSource source = new FileDataSource("c:\\prova.txt"); 
messageBodyPart1.setDataHandler(new DataHandler(source)); 
messageBodyPart1.setFileName("c:\\prova.txt"); 
multipart.addBodyPart(messageBodyPart1); 
messageBodyPart2 = new MimeBodyPart(); 
DataSource source = new FileDataSource("c:\\pippo.txt"); 
messageBodyPart2.setDataHandler(new DataHandler(source)); 
messageBodyPart2.setFileName("c:\\pippo.txt"); 
multipart.addBodyPart(messageBodyPart2);