DropBox is best bet, get as many of the discs in the 2gb as possible, once full then copy it to your hard disk and delete whats in the dropbox and start all over again with the remaining disks.
An alternative is to use Mixcloud – its free and a user can upload as many mixes as they wish. However, the file size limit is 100mb and has to be MP3. You could get your mate to upload his mixes a disk at a time, though when he rips them to mp3 he will need to adjust the quality setting. I use LAME to encode to mp3 from audacity and the VBR setting 2 or 3 should get a cd length mix under 100mb. My most recent mix was an hour and a half and I got that down to 96mb using setting 4 or 5 and even that sounds good through my hi-fi speakers.