Calling Matlab code from java app running on the internal jvm

I have to integrate some java code into my matlab code to do a few things that, as far as I know, matlab can't, like directly communicating with a html web page. For this to work I need to call the java code from matlab, which is easy, and call matlab code from java.

When googling the problem I found a few approaches that allowed java controll matlab. But all solutions talked about the java running on a different jvm. Can java running on the internal jvm directly call matlab? And if I call java from the html code, does execute on the matlab jvm?