Bind ngInclude to different models

Is it possible to specify model for ngInclude so that any changes done inside the included template are reflected on the specified model. For instance:

I have a model such as :

$scope.member = {

    name: "Member1",
    children:[
    {
        name:"Child1"
    },
    {
        name:"Child2"
    }
    ]
};

and the template:

<script type="text/ng-template" id="name.html">
    <input type="text" ng-model="member.name"/>
</script>

Now is it possible to pass ngInclude either "member" or any child and get their respective name properties modified? I tried passing ng-model to the ng-template but it doesn't work. I tried to dynamically load the scope with the intended model but if the model gets delete, I am left with an orphan template. Following is the jsfiddle code:

http://jsfiddle.net/vaibhavgupta007/p7E5K/

I wish to reuse the template rather than duplicating the same template for different models. I have refered to this question:

How to specify model to a ngInclude directive in AngularJS?

But here models are not getting deleted.

Edit

I have not grasped the concepts of creating custom directives till now. But will creating a new directive in conjuction with ng-include help?

The answer of your last question is: yes. In a directive, you define also a template and a scope. The content of the scope is completely in your hands.

See here: http://jsfiddle.net/vgWQG/1/

Usage:

Member: <member model="member"></member>
<ul>
    <li ng-repeat="child in member.children">
        Child {{$index}}: <member model="child"></member>   
    </li>
</ul>

The directive:

app.directive('member', function(){
return {
    template : '<input type="text" ng-model="member.name"/>',
    replace : true,
    restrict: 'E',
    scope : {
        'member' : '=model'
    },
    link: function(scope, element, attr) {}
};

});

I've moved the template in an inline variant because I could not getting the template cache getting to work in jsfiddle. In a real world, a templateUrl: 'name.html' should be fine.

This is what you want?