<p>Current url = {{url}}</p>

app.controller('MainController', function($scope) {
    // This is the inital url
    // It shows up in the HTML fragment
    $scope.url = "http://stackoverflow.com";
});

webview.addEventListener('loadcommit', function() {
  url = webview.src;
  //How to update Angular framework with current value of url?
}

$scope.url = url;

<div ng-controller="MainController">
    <webview current-src="url" id="foo"
             src="http://stackoverflow.com/"
             style="width:640px; height:480px">
    </webview>

    <p>Current url = {{url}}</p>
</div>

app.directive("webview",function() {
    return {
        restrict: "E",
        link: function(scope,elem,attrs) {
            var webview=elem[0];
            elem.on("loadcommit", function(e) {
                $scope.$apply(attrs.currentSrc +'='+ webview.src);
            };
        }
    };
});