First off, I'm not a native speaker but this question isn't about the rules themselves but rather usage in the USA.
I learnt that you should say 'unhealthier' (and the Oxford + Longman dictionaries I looked up back me up), but an acquaintance of mine (native speaker) told me to change because it was wrong, it should be 'more unhealthy'. When I pointed out the dictionary backs 'unhealthier', he dismissed the issue as both being accepted but 'more' is still the preferred option in the States and that I should still change.
So what's the story? Are both academically accepted (this person writes/speaks in a very informal way)? Is 'more unhealthy' really so preferred in the States that 'unhealthier' becomes deprecated?