Really depends on how much data we are talking about. I think dropbox offers about 5GB of free storage now. If you can get your customer to use it you can easily share different folders with different accounts. (But that might be problematic with some companies security policies)
Personally I have set up webpages for different people to share the media with. Also has the upside that you have more options and can actually easily implement a nice looking gallery. But getting that setup for free is going to be tricky. But for a few € per month you should be able to get an okay set up.
Although normally I would not touch 1&1 with a stick I have to say their webservices are pretty good and very reliable, you might want to check them out. Their Smartweb L (3,99 per month) or 1&1 Dual Basic (6,99 per month, careful, they sponsor the first 12 months that's why it says 3,49 on the webpage) might be suitable. You wont have a lot of webspace though, so it really again depends on the amount of data you have. I am sure there are cheaper alternatives out there, but I only have 1&1 experience personally.
