Are you transferring the file, or is the VB application? The simplest thing I can think of is if you have Samba installed on the Unix box, you should be able to configure shares that are visible to the Windows box the app is running on, then just save/copy the html file to the share.
Otherwise I think you'd have to invoke an FTP routine (assuming FTP is running as a server on the Unix box) and possible send it that way. Given it sounds like it is a web server, is FTP running on the box? Or maybe scripting or calling SCP (if it's using secure communications)?
Maybe some one else has some thoughts, that's what came to mind for me. I'm only learning .NET myself, so I can't really help with any code, but perhaps this might trigger some discussion or ideas from someone else.