What is a word to describe someone who is not a Protestant? I've been wondering for a while if there is a word (or concise phrase) that can be used to mean someone who is not Protestant. Something that specifically groups Catholics, and Eastern Rite followers (Orthodox churches). But hopefully that does not include such groups as the Mormons or Jehovah's Witnesses for example (which are not Protestant nor even trinitarian/monotheistic). Is there such a term? Is there one that does include these last two groups? 

The obvious choice would be "non-Protestant", but is there a better term than this? Since, technically, atheists and Muslims are also non-Protestants.



edit:

In the comments, I propose a term that could convey that message, but that seems to be getting a different usage:


Patriarchal Churches


Which then makes me wonder if something like


Patriarchal Rite Churches


would be a good candidate to describe this grouping. I don't think I've ever heard of a Protestant denomination having a Pope or Patriarch. Even the hierarchical ones.
I believe the correct answer is that there is no such term that has attained any significant level of recognition. 

That said, the largely unrecognised terms Ancient-rite Christians / Ancient-rite Churches may be suitable for what you are seeking although they wouldn't exclude Oriental Orthodoxy if that is an important distinction. 

We could no doubt multiply potential alternatives eg. Pre-Reformation Churches, Apostolic Successionists, 7-Council Churches (Adherants of the Seven widely recognised Ecumenical Councils); but they are, in the main, no less problematic and considerably clumsier, including your suggestions of Patriarchal Churches / Patriarchal Rite Churches which could perhaps be viewed as technically descriptive, but are more likely to be confusing given the very different roles Patriarchates now play within the Traditions in question.

For almost any term you select, there will most likely be Traditions, sects or denominations that will challenge it's validity - eg. considering where the Czechoslovak Hussite Church fits in is always going to be problematic.