So far tvOS supports two ways to make tv apps, TVML and UIKit, and there is no official mentions about how to mix up things to make a TVML (that is basically XML) User Interface with the native counter part for the app logic and I/O (like playback, streaming, iCloud persistence, etc).
So, which is the best solution to mix TVML and UIKit in a new tvOS app?
In the following I have tried a solution following code snippets adapted from Apple Forums and related questions about JavaScriptCore to ObjC/Swift binding. This is a simple wrapper class in your Swift project.
import UIKit
import TVMLKit
@objc protocol MyJSClass : JSExport {
    func getItem(key:String) -> String?
    func setItem(key:String, data:String)
}
class MyClass: NSObject, MyJSClass {
    func getItem(key: String) -> String? {
        return "String value"
    }
    func setItem(key: String, data: String) {
        print("Set key:\(key) value:\(data)")
    }
}
where the delegate must conform a TVApplicationControllerDelegate:
typealias TVApplicationDelegate = AppDelegate
extension TVApplicationDelegate : TVApplicationControllerDelegate {
    func appController(appController: TVApplicationController, evaluateAppJavaScriptInContext jsContext: JSContext) {
        let myClass: MyClass = MyClass();
        jsContext.setObject(myClass, forKeyedSubscript: "objectwrapper");
    }
    func appController(appController: TVApplicationController, didFailWithError error: NSError) {
        let title = "Error Launching Application"
        let message = error.localizedDescription
        let alertController = UIAlertController(title: title, message: message, preferredStyle:.Alert ) self.appController?.navigationController.presentViewController(alertController, animated: true, completion: { () -> Void in
            })
        }
    func appController(appController: TVApplicationController, didStopWithOptions options: [String : AnyObject]?) {
    }
    func appController(appController: TVApplicationController, didFinishLaunchingWithOptions options: [String : AnyObject]?) {
    }
}
At this point the javascript is very simple like. Take a look at the methods with named parameters, you will need to change the javascript counter part method name:
   App.onLaunch = function(options) {
       var text = objectwrapper.getItem()
        // keep an eye here, the method name it changes when you have named parameters, you need camel case for parameters:      
       objectwrapper.setItemData("test", "value")
 }
App. onExit = function() {
        console.log('App finished');
    }
Now, supposed that you have a very complex js interface to export like
@protocol MXMJSProtocol<JSExport>
- (void)boot:(JSValue *)status network:(JSValue*)network user:(JSValue*)c3;
- (NSString*)getVersion;
@end
@interface MXMJSObject : NSObject<MXMJSProtocol>
@end
@implementation MXMJSObject
- (NSString*)getVersion {
  return @"0.0.1";
}
you can do like
JSExportAs(boot, 
      - (void)boot:(JSValue *)status network:(JSValue*)network user:(JSValue*)c3 );
At this point in the JS Counter part you will not do the camel case:
objectwrapper.bootNetworkUser(statusChanged,networkChanged,userChanged)
but you are going to do:
objectwrapper.boot(statusChanged,networkChanged,userChanged)
Finally, look at this interface again:
- (void)boot:(JSValue *)status network:(JSValue*)network user:(JSValue*)c3;
The value JSValue* passed in. is a way to pass completion handlers between ObjC/Swift and JavaScriptCore. At this point in the native code you do all call with arguments:
dispatch_async(dispatch_get_main_queue(), ^{
                                           NSNumber *state  = [NSNumber numberWithInteger:status];
                                           [networkChanged.context[@"setTimeout"]
                                            callWithArguments:@[networkChanged, @0, state]];
                                       });
In my findings, I have seen that the MainThread will hang if you do not dispatch on the main thread and async. So I will call the javascript "setTimeout" call that calls the completion handler callback.
So the approach I have used here is:
- Use 
JSExportAsto take car of methods with named parameters and avoid to camel case javascript counterparts like callMyParam1Param2Param3 - Use 
JSValueas parameter to get rid of completion handlers. Use callWithArguments on the native side. Use javascript functions on the JS side; dispatch_asyncfor completion handlers, possibly calling a setTimeout 0-delayed in the JavaScript side, to avoid the UI to freeze.
[UPDATE]
I have updated this question in order to be more clear. I'm finding a technical solution for bridging TVML and UIKit in order to 
- Understand the best programming model with 
JavaScriptCode - Have the right bridge from 
JavaScriptCoretoObjectiveCand viceversa - Have the best performances when calling 
JavaScriptCodefromObjective-C