The .NET Framework implements a WebBrowser-object (System.Windows.Forms.WebBrowser), which could be used to implement a web browser in an application.
SharePoint itself, uses to different methods, to display a combobox for fields of the type "lookup". When the looked up list contains less than 20 items, a simple html-combobox is used. The the list contains 20 items or more, SharePoint uses an ASP.NET-control for the combobox.
As you can see, the comboboxes look different.
When you use SharePoint with the Internet Explorer, everything behaves as expected. When you use the WebBrowser-object from the .NET Framework, it is not possible to select items from the ASP.NET-combobox. Every click in the selection-list closes the list and nothing is taken to the textbox.
It seems, as if there is a bug in the WebBrowser-class in the RTM of the .NET Framework 2.0. When you install the Service Pack 1 or the .NET Framework 3.5, the WebBrowser-object behaves as expected, and you can use the ASP.NET-comboboxes on SharePoint-pages.