If I understand the situation correctly, yes, this can be done in ASP.NET.
The easiest way to set this up is to create a HTML table with the tabs and a few panels that contain the datagrids.
Each cell in the tab table contains a single tab with a hyperlink control. As soon as the hyperlink is clicked, a server side event is triggered. Inside the event, you can find out which tab was clicked and then hide all panels containing the grids and only show the right panel and datagrid for the current tab. You can then set the "selected" style for the current tab to make it appear selected.
The IBuySpy example (available from http://www.asp.net/Default.aspx?tabindex=5&tabid=42
) shows how you can do this.
In fact, the whole ASP.NET site is based on this principle.