Back in 2008, I did some research on this topic, together with Achiel. That was in the Mendix 2.4.0 days. ;-) While trying to do so, we discovered something that we actually already knew.. The Mendix runtime is an application server itself.
Trying to run Mendix inside Websphere is as difficult as trying to run JBoss in Websphere, or to run Websphere in Tomcat. It possibly can be done, but it needs a huge rewrite of many core parts of the product only to adjust it to work together with that specific other application server.
If Websphere is your application server to deploy java code, then Mendix is your application server to deploy a mendix application model.
I guess the current 'viewpoint' is not that different from back then.