Question: I read that a page which runs under an https connection cannot share an InProc Session (based on cookies) with another page (or the same for that matter) running under regular http. My site is running on Server 2003, IIS 6 and .Net 2.0.

After some experiments it appears that a page which stores data in session while being connected through https CAN subsequently access the data even if running under plain http.

So, is it possible or should I go over and look for flaws in the SSL configuration?

Answer: 
*IIS setting
In the IIS properties window, under the ASP tab –> Session Properties, there is a setting for “New ID on Secure Connections”* 

I fixed this intermittent issue for myself by setting this to false.
Searching for the problem doesn't turn up much chatter about it so far, still looking.

*Edit*: okay finding some stuff now.

Right it seems that it will work fine if both sets of pages are in the same application/website.

So I'd go ahead and carry on, feeling reassured.