First, this has grave potential security consequences that you'll need to have your eyes open about.
Do you have a static IP address? If so then if you set your not then you'll need a service such as DynDNS running on some machine on your LAN so your access attempts can be routed to whatever your IP address happens to be at the moment.
(If that paragraph doesn't make sense to you, stop right now.)
Then go to Airport Utility and check mark the "Share disks over WAN" option in the Disks tab. Be sure to set a strong password and manually encrypt anything of value on that disk... or any other disk you have attached, including your Time Machine backups, as all disks will be shared.
I assume you're trying to steam video to the Infuse App(?) Unless you've got a good upstream link on your broadband (probably 1-2Mbit/sec minimum) you'll struggle to get something you're happy with unless the bit rate is low.
Have you looked at other streaming solutions (like Plex)? These will be a much slicker solution not to mention more secure than opening up your Airport Extreme disk completely to the Internet.
If you have enough space on your iPad, Infuse can copy your content locally for offline viewing.
If not, Plex will do everything you've asked for. But if you really don't want to run that, maybe a steaming solution like Netflix, Amazon Prime etc would be better for you and there is no complexity involved.
If you don't mind geeking out a bit, you can set up a Plex server using a $35 Raspberry Pi 2, with a USB disk (connected to a powered hub) to hold your media. Works a treat. It'll be a project to get it going, but a fun one if you're a bit of a nerd at heart.
I've looked into this but due to the CPU constraints of the Pi 2 it isn't capable of transcoding and is best suited for serving up content locally.
I am considering using a Pi as a client in one of my rooms though as I don't need a full blown Apple TV there.