Yes, we share sesseion because it both are microsoft
technology and asp.net is next generation of asp.

Cookies are the most common way for Web applications to 
identify the user session, and can be used to identify 
session state for both classic ASP and ASP.NET. Session 
state information is stored in memory in ASP script and 
can't be shared with other applications, such as ASP.NET. 
If the session state is stored in a common format in SQL 
Server, the session state can be accessible by both classic 
ASP and ASP.NET.