var inAppBrowserRef = cordova.InAppBrowser.open("http://www.mypage.com", "_blank");
inAppBrowserRef.addEventListener("message", function (params){
    if(params.data.action === "myNativeMethod"){
        // Call your native method
        myApp.myNativeMethod();
    }
});


//Then in the webpage being loaded into the InappBrowser you'd send the message:

<button id="myButton">Press me</button>
<script type="text/javascript">
    document.getElementById("myButton").addEventListener("click", function(){
        var message = {action: "myNativeMethod"};
        webkit.messageHandlers.cordova_iab.postMessage(JSON.stringify(message));
    }, false);
</script>

//If you don't have direct control over the page being loaded into the InappBrowser, you could inject the code to send the message:

inAppBrowserRef.executeScript({ 
    code: '\
        document.getElementById("myButton").addEventListener("click", function(){\
            var message = {action: "myNativeMethod"};\
            webkit.messageHandlers.cordova_iab.postMessage(JSON.stringify(message));\
        }, false);\
    '
});