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I can't think of a possible situation that you may have a problem having two different passports, both from major first-world countries. You'll be OK.
What if all of our travel documents were stolen? Would we all end up at a different consulate than her?
If your documents are stolen, you both go to police, get a copy of your police report, and go to American consulate first, then to Canadian consulate. At both places, you apply for temporary documents to return home. You don't have to be separated from each other.
Or, say we were accused of doing something illegal in one of those countries.
There is no benefit or disadvantage from being of the same nationality when you are accused of a crime.
You problems may arise if you are from a first-world country and your companion is from a third-world country. You may be admitted to enter the country, while she may be denied entry. So you'll need to be separated, because you are already inside the country but she'll be put on the return flight.