The larger problem I see with regards to REST is: what resource are you hitting that would give you multiple types? Meta resources like /media, /things, etc aren't ideal; is there a better way to do it?
I am not sure that this is the canonical approach, but the way I did it was to model my search index as the resource. Requesting it with no parameters returned the entire index in its natural sort. Additional parameters filtered/sorted/paged/etc.