Extending $resource of angularjs using IResourceClass of typescript

First define your model, the interface that will describes your employee.

// Define an interface of the object you want to use, providing it's properties
interface IEmployee extends ng.resource.IResource<IEmployee>
{
    id: number;
    firstName : string;
    lastName : string;
}

Then create an interface that describes the resource you will create.

// Define your resource, adding the signature of the custom actions
interface IEmployeeResource extends ng.resource.IResourceClass<IEmployee>
{
    update(IEmployee) : IEmployee;
}

Create the EmployeeResource factory:

var myApp = angular.module('myApp', ['ngResource']).factory('EmployeeResource', 
    ['$resource', ($resource : ng.resource.IResourceService) : IEmployeeResource => {

        // Define your custom actions here as IActionDescriptor
        var updateAction : ng.resource.IActionDescriptor = {
            method: 'PUT',
            isArray: false
        };

        // Return the resource, include your custom actions
        return <IEmployeeResource> $resource('/api/employee/:id', { id: '@id' }, {
            update: updateAction
        });

    }]);

Inject your EmployeeResource into a controller:

myApp.controller('TestCtrl', ['$scope', 'EmployeeResource', ($scope, Employee : IEmployeeResource) => 
{
    // Get all employees
    var employees : Array<IEmployee> = Employee.query();

    // Get specific employee, and change their last name
    var employee : IEmployee = Employee.get({ id: 123 });
    employee.lastName = 'Smith';
    employee.$save();

    // Custom action
    var updatedEmployee : IEmployee = Employee.update({ id: 100, firstName: "John" });
}]);