The first suggestion would be to use the MS-recommended method for robust/automated deployment - Web Setup projects [1, 2].
One other alternative would be to utilize the VBP Copy Files (if the server is on the same network) or FTP actions (if the server is only FTP-accessible) to copy the files.
Otherwise, a couple possibilities for automating the VS.NET GUI would be
1) Try recording a macro in the IDE for the Copy Files dialog [3] to see if a programmable method to perform that is available, and invoke devenv from the build [4] to run the macro that calls the necessary methods
2) Call a tool such as AutoIt [5] or Macro Magic [6] from the build to control the VS.NET IDE and invoke the Copy Files dialog.
[1]
http://msdn.microsoft.com/library/en...Deployment.asp
[2]
http://www.15seconds.com/issue/030806.htm
[3]
http://msdn.microsoft.com/library/en...udioMacros.asp
[4]
http://msdn.microsoft.com/library/de...lrfcommand.asp
[5]
http://www.hiddensoft.com
[6]
http://www.snapfiles.com/get/macromagic.html