Inter Application Communication between Web Application embedded in an Other Web Application

I have a situation where I have one Web Application embedded in a second Web application. Both applications are stateless. The embedded application has buttons and links and the user does any number of tasks in the embedded application. When the user finishes the workflow in the embedded application there is information returned to the client (web page) the the parent application needs to know about (this could also happen for intermediate steps in the process of the embedded application). I'm thinking embedding the application is easy enough (iframe) but what is the best way to get data from the embedded application (static html on the web page) to the parent application? I have some control over the embedded application (it is an application developed by an outside organization that we are paying for) and full control over the parent application (we are building it).

I'm thinking something like expecting the embedded application to provide the data I'm looking for in a specifically named div and using javascript to fish the data out.

<div id="DataOutterApplicationIsLookingFor">The data I'm looking for</div>

I imagine there is an event associated with the activities that will occur as the user clicks through the embedded application I can use as triggers to look for the named div and the data I need.