Jasonette is currently targeted at building mobile apps primarily.
There IS an option to take your web app and turn it into a mobile app first just to get started, and then slowly switch out multiple components in the app into native, as mentioned in this article https://medium.freecodecamp.org/how-to-turn-your-website-into-a-mobile-app-with-7-lines-of-json-631c9c9895f5
And there is a Jasonette-Web project that's meant for replicating the UI aspect (https://github.com/Jasonette/Jasonette-Web and http://web.jasonette.com/) and you will be able to generate a web UI that looks the same as the mobile apps, but in terms of actual application logic, those are not yet implemented, since it's hard to replicate native iOS and Android APIs inside a browser. There maybe workarounds and we may explore some of these options in the future.
That said, a recommended way is to build them separately. You want to present good user experience for both web and mobile, so you should build for web using web's native language which are (html+JS+css), and on mobile build natively (with Jasonette for example)