I'm surprised to not see Plex mentioned yet. Plex is both a media server, front end GUI for watching on a computer and mobile app for streaming content from your media server. It is extremely straight forward to set up both for at home use and remote streaming via a free Plex account. The computer version is free and the iOS app is $5.
You can download Plex for your PC at https://plex.tv/downloads and Plex for your iOS device at https://itunes.apple.com/us/app/plex/id383457673?mt=8
I've used both for 3-4 years now, often to watch content stored at home while traveling, with little to no complaints.
With that said. I know that Plex can connect to your iTunes library and play it through the home theater interface but I don't know that this same functionality is present in the iOS app.