I actually set up a document using Berthold Regular as a paragraph style then copied and pasted into a new one, and it went over just fine, with no problems.
The only other thing I can think of is perhaps some font issue with your font management program. Go to your original document and select a text box that has the Berthold Regular style. Now with that text box selected, look at your character palette. Under the font name, where it says "regular", are there brackets around "regular"? If so, this indicates that even though you set it to regular, regular is not actually activated on your computer--which might make sense with why it's changing in a new document--cuz technically, you're "attaching" something to it, that doesn't "exist" (since it's not active). ...but if there are no brackets, then you should be all set.
Please post a solution if you find one. This would be good to know for the future.