Home Sharing allows you to share music from a computer to another computer or device, it doesn't work between just devices, it needs a computer.
Home sharing : http://support.apple.com/kb/HT3819
You could potentially log in with your account on his iPad and re-download your music (if you are in a country where music can be re-downloaded), but you risk tying his iPad to your account for 90 days (so it's probably not worth it) : http://support.apple.com/kb/HT4627
You can't inherently share music with each other if you have different ID's. Home sharing works from your iTunes library on a computer so without a desktop, you cannot home share. You also need to be signed into the same ID on the iPad as the home library in order to share.
You can sign into each other's ID's on your respective devices and download the music using each other's ID, but that will lock you out of your own ID for 90 days. Purchases made with different ID's are really not meant to be shared.