I have sometime seen the argument for Node of using the same code on client and backend simultaneously, but in practice I haven't found any use for that. The only big thing I can think of is form/model validation, but if you do ajax, you can just as well do all that on the server anyway.
I recently re-wrote my blog (https://blog.cesarandreu.com/) to take this approach. Repo: https://github.com/cesarandreu/trois-blog
The client bootstrap code that's used on the server is in client/middleware.js. Aside from that it reuses the exact same code.
In practice though (and if you're using the nodejs), you would have better organization... for ex, all of your nodejs code for in a directory, and then a directory with your templates (which is also where the inline client side js would go). Making it much easier to think about them separately.