You have two options:
Create a LabVIEW Remote Panel: http://www.ni.com/tutorial/4791/en/http://www.ni.com/tutorial/4791/en/ , OR Set up a Windows Remote Desktop connection, to let your supervisor log into your PC: http://windows.microsoft.com/en-au/windows/connect-using-remote-desktop-connection#connect-using-remote-desktop-connection=windows-7
Option #1 is more secure.
Note: Option #2 doesn't use a HTML file, while Option #1 does. However, you don't convert your program into HTML. Instead, you create a HTML file to let your supervisor control your LabVIEW program through the Internet. You must still run your LabVIEW program on your local PC.