I want to use Node.js as a Share.js server and Ruby for the frontend. As far as I know, Heroku only allows one web-facing process called "web". Does anyone have some experience trying to do something like this?

No, Heroku detects the application type when you push your code to Heroku and it compiles the slug. You'd need to have them as seperate applications with a defined API between the two (not always a bad thing)

UPDATE: You can 'stack' buildpacks these days, eg Ruby + PHP so you could have both executed. See https://devcenter.heroku.com/articles/using-multiple-buildpacks-for-an-app for how to use multiple buildpacks in the same app.