How to change mime types on Azure CDN

For a website we are using a Azure CDN (standard) backed with an Azure blob storage for the static content. All static content is served correctly, except Woff and TFF files, which are not served to the websites, and getting a 404. All other content from the same folder is served

If I load the static content from the blob storage itself (not using the CDN), I have the same problem.

In IIS I would fix this, by adding the woff, woff2 and tff to the MIME types, but for an Azure CDN or blob storage I can't figure it out how to configure this.

So my questions are: How can I expose the woff, woff2 and ttf types to my websites using an Azure CDN?