How use same Behavior Drive Development (BDD) stories across platforms?

I'm writing an app that has a client for iOS, Android, and the web. The server is hosted on Google App Engine (Java). REST is used for the communication between clients and server.

In order to ensure a uniform user experience across platforms, as a software designer, I want to write Behavior Driven Development (BDD) stories in one text file and have them drive development at every layer of the stack.

One partial solution for the Android client and the server is JBehave because it supports Java. But the iOS client is written in Objective-C and some Swift which JBehave can't help with.

What I like about JBehave though is it allows me to write stories in a simple syntax and keep those stories in a text file. It can be the same text file for every developer, regardless of their layer of the stack (as long as it's a Java developer).

I found some BDD frameworks for iOS at http://ift.tt/1svbbkr. But after skimming their documentation sets, I can't find any that emphasize a simple file format like JBehave's. As a designer, I don't want to write in some format that's partially story and partially code. That's too much syntax for me to have to learn AND risks inconsistencies cropping up across the different manifestations of the stories.

Moreover I haven't found any frameworks that discuss their portability across different layers of the stack and/or across development platforms.

How can I achieve the maximum potential of BDD in a heterogenous development environment?