Play MIDI files on iPod touch

My son's drum teacher gave him a bunch of MIDI files to practice drums with. I loaded the Sweet MIDI player app on his iPod touch so that he can listen to them through headphones. How do I get those MIDI files onto the iPod Touch? I'm familiar with adding music to my library in iTunes using the File, Add File to Library command in iTunes, but when I use that to import these MIDI files they never appear in my iTunes library. Without having them in iTunes I can't find a way to get them onto the iPod. What is especially perplexing is that the Sweet MIDI app came with a group of MIDI files. We can view and play them from within the app on the iPod Touch, but when we connect that iPod to our PC and open iTunes those MIDI files do not appear anywhere in the On This iPod section with the rest of his music files. So, it's clear that MIDI files can be played by the Sweet MIDI app on an iPod touch, I just can't figure out how to put any MIDI files on it except for the ones that came with the Sweet MIDI app. Can anyone help?

We're using a 4th generation iPod touch with iOS 6.1.3; Our PC is running Windows 7 and iTunes version 11.0.2.26.