I have created a node.js application in Visual Studio 2015 using the Azure SDK 2.7 and the Node.js Tools.
I have successfully set up CI with BitBucket in my web app
Also when you deploy the zip file via the azurewebsites.net/ZipDeployUI, make sure that you see the files being unzipped on the /wwwroot level.
If the files show up under /wwwroot/your-app-folder/ you may get this permission issue. I took a long time to figure this out! Hope it helps.