Reproduce
Using our [example code](
http://docs.appcelerator.com/platform/latest/#!/guide/Communication_Between_WebViews_and_Titanium-section-29004919_CommunicationBetweenWebViewsandTitanium-Ti.AppEvents) from document, we can make a communication between WebViews and Titanium. But on IOS and Android bidirectional communication is working fine (from titanium to web view and from web view to titanium). But in mobile web from web view to titanium only working. The reverse is not working(from titanium to web view).
Test Code
See the document.
Marking ticket as "Won't Fix" as MobileWeb has been deprecated.