An HTTP server is able to serve HTML and XHTMl among other content types.
IIS either supports ASP processing out of the box or as an official extension.
Apache Tomcat is primarily a JSP/Servlet container and also doubles up as an HTTP server.
Looks like there is an IIS plugin for Apache Tomcat. (Google for "iis tomcat plugin"). So you could use the HTTP capability of IIS in combination with JSP/Servlet processing capabilities of Apache Tomcat.
There is an Apache Tomcat module for the Apache Web server called mod_jk. So you can use the HTTP capability of the Apache web server in combination with JSP/Servlet processing capabilities of Apache Tomcat.
Finally, If there's an IIS plugin I guess any java application server can be considered compatible with IIS.