A portion of our site is done in PHP and a portion of our site is done in ASP.Net. We just set up a new web server with Windows Server 2008 R2 which has IIS 7.5 installed.>
Yes you can, but watch out for this:
If you have a wordpress on your "root", and asp.net apps in folders under it
(e.g. http://root.com/aspnetapp1/), and if you follow these suggestions about "urlrewrite" for permalinks in wordpress, you can have trouble if you try to configure "wildcard handlers" in the apsnetapp1.
To avoid issues, the web.config of the wordpress root app must also have that setting:
...
Or else, your wildcard handler will never raise because index.php from root will catch all your requests to url like: http://root.com/aspnetapp1/api/*