That is, is it possible to have cards where each side can function as the front side of the other?

For example, I might want to recall a sentence given its translation in the other language

DE: Unsere Mütter sind starke Frauen.
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EN: Our mothers are strong women.

Yes, there is a setting you can turn on either globally, per deck, or per card called "Review in reverse". When that setting is on both front-to-back and back-to-front versions of the card will appear in the review session.

https://mochi.cards/docs/reviewing/review-reverse/