angular ng-bind-html and directive within it

I was also facing this problem and after hours searching the internet I read @Chandermani’s comment, which proved to be the solution.
You need to call a ‘compile’ directive with this pattern:

HTML:

<div compile="details"></div>

JS:

.directive('compile', ['$compile', function ($compile) {
    return function(scope, element, attrs) {
        scope.$watch(
            function(scope) {
                // watch the 'compile' expression for changes
                return scope.$eval(attrs.compile);
            },
            function(value) {
                // when the 'compile' expression changes
                // assign it into the current DOM
                element.html(value);

                // compile the new DOM and link it to the current
                // scope.
                // NOTE: we only compile .childNodes so that
                // we don't get into infinite loop compiling ourselves
                $compile(element.contents())(scope);
            }
        );
    };
}])

You can see a working fiddle of it here