You can open both PDFs in Acrobat and go to Tools> Organize Pages, (if they open as tabs, you can drag one tab away from the other to view both PDFs at the same time), you can drag page one of the translated PDF to the page 2 position of the original PDF, and repeat for all of the other pages, save to a new name and then go to File> Properties> Initial view> Page Layout> Two-up facing, save. It's not automatic, but pretty straight forward.
Yes, There's only one way you can do, is that split pages the translated file and the original file and give a appropriate (page number wise) file name and than do combine the both files of split pages accordingly (i.e., if the translated split file name is 1 than the original file name should be 1a or 1.1).
To always show both pages next to each other (regardless of the configuration of your Acrobat or Adobe Reader), you would need to use an "imposition" tool that would allow you to combine both source pages on one target page. If this is something you need to do on a regular basis, it may be worth investing in such a tool. The one that I've used for probably 15 years is Quite Imposing Plus (http://www.quite.com).
Hey, it's an InDesign forum, after all... [EDIT: uups, seems it's not ]
I believe try67's script is awesome, however, here's zero budget solution, too.
Just a bit more manual work, as it happens.
Not a big deal, if this is something you need to do just occasionally.
1. Create new indd doc with non-facing pages and page size identical to your pdfs page size.
2. Place your original pdf. Better use Scott Zanelli's MultiPageImporter2.5.jsx script (can be found here) or anything similar to place multipage pdf into ID.
3. Save indd file, say, Original.indd.
4. Rinse and repeat steps above with your Translated pdf, save as Translation.indd. Both docs must have the same page size and equal page count!
5. Go to this thread, install script from the post 27 (the last one).
6. Run that InterleaveDocs script with both your docs (original and translated) open.
7. New merged document is created, both originals closed by script.
8. With your new merged doc open, go to Page Setup, change Start Page #: 2 and check Facing Pages ON.
9. Now you can export new pdf with Original and Translation side by side, just don't forget to enable Spreads on export...