The word 'session' can be a little confusing in ASP.NET.
If you are talking about security (authentication and authorization), you are probably looking for a Single Sign-On solution. In other words, when a user logs into one site they won't be prompted to log into another related site. Take a look at Windows Identity Foundation, OAuth, Jasig CAS. CAS is my preferred solution (I'm a developer on the .NET client), but the server is written in Java and you'll need some expertise with Java to get it configured the way you want.
In ASP.NET, Session state is a completely separate component from authentication and authorization (although it can depend on the result of the authentication step). If you are trying to share information between the 2 sites (i.e., shopping cart contents), you can either configure both domains to use the same database as a Session provider (google aspnet_regsql -ssadd) or you can just store the data in a database that is accessible by both.
For more info on why I emphasize the distinction, check this out: http://www.codeproject.com/KB/aspnet/ASPDOTNETPageLifecycle.aspx
Good luck.