As some others have commented, the best way is likely to be for you to create your own content server. It really isn't hard and I expect you will find a number of organisations that will provide one very cheaply - maybe as low as a few USD per year.
Look for one that offers easy setup of a content management service (CMS) such as WordPress or Joomla or even better for your needs, OwnCloud.
Then you can upload your files there and download them wherever you need them. Indeed, why not make it even easier and ditch the "files" altogether and use web pages instead if you can.
One thing to watch out for is smart filtering devices that your employer might use, these may be smart enough to learn that your site is untrusted and block it from up/downloading files anyway. That's another reason to switch from files to web pages since those are far less likely to get blocked.
It should not need to be said that you need to take care with the information you handle this way and only ever use personally created content that your employer or anyone else cannot lay claim to. Check your terms of employment for any clauses that might mean anything you create in the job doesn't belong to you.
Having said that, if they are really not that bothered, you are unlikely to have an issue as long as you can demonstrate the value and ensure that the content is legally and morally shareable.
Owndrive is based in Norway and has a free tier for OwnCloud so you could try it out and nothing lost if it doesn't work. There is a longer list of providers including a decent list of free ones on the OwnCloud website.
Bluehost are supposedly both reliable and cheap for Wordpress and other hosting. Costing just a few dollars per month. If you can get away with plain WordPress then wordpress.com have a free tier.