You might want to ask how session variables are saved in the ASP forum. PHP generally saves session variables the designated temp directory, and they are simply text files with serialized data. I don't know how ASP saves session vars.
Your best bet is probably to make your own "homegrown" session manager, which stores session keys and data in a database. Sessions are essentially a simple mechanism, so it shouldn't be too hard to do. As long as your variables are simple strings or numbers, it shouldn't be too difficult to save them from one environment and read them in another.
Here is a link to an article about customizing session handlers in PHP, to save to a database:
I don't know if this kind of thing is necessarily the answer, since it will still serialize your variables as it writes them to the database. Also, as I said, I don't know if ASP offers the ability to directly interact with its session handling mechanism.
But, essentially, you can do it yourself. On the beginning side, just set a unique ID key with a good randomizing function, and save your server-side data associated with that ID. You can save it in a database table which stores ID keys and the variables, and then just have the other environment read from that database.
If you are trying to transfer complex variables, such as arrays, you will have a problem. You might want to try the WDDX library, because it offers ways to serialize variables accross programming environments. I have never used it, though, so I can't offer any real help there.