At the moment ASP.NET and Silverlight are two different sets of technology. If you want to build an ASP.NET application you would use an ASP.NET Project, if you want to build a Silverlight application you would use a Silverlight project and integrate with ASP.NET.
Silverlight could fit in really well with ASP.NET (but currently doesn't). However in ASP.NET 3.5 this started to change. There are now 2 Silverlight based ASP.NET controls which you can drop onto your regular Web Form (Silverlight and Media Player).
ASP.NET The Future (my guess)
If I were to take a punt into the ASP.NET Silverlight future this is where I would guess the ASP.NET framework is going (p.s. I have no actual insight into this, I am just taking a guess). Slowly but surely I reckon more and more Silverlight based ASP.NET controls will be made available to drop into your designer.
A real easy guess is that a Deep Zoom control will become a standard control on the ASP.NET designer. There is no reason that you couldn't start to develop such controls yourself (and I encourage you to do so), however I think/hope that one day they will be made available as standard controls.
So in my next article I will discuss in more details where else I think ASP.NET will change to accommodate Silverlight (including modifications to existing controls) not just new ones.