You're correct about it being sort of awkward at first when you are figuring out how to structure an isomorphic applications. It gets even weirder when you only use JavaScript as a compilation target.
I created an example isomorphic Clojure and ClojureScript application (https://github.com/domkm/omelette) and wrote about how it works (http://domkm.com/posts/2014-06-15-isomorphic-clojure-1/). It was an interesting experience. I wouldn't recommend it for production quite yet but I'm looking forward (and working toward) the day when we can easily deploy isomorphic applications that are not written in JavaScript.