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Counterpoint written so that the voices can be swapped — the upper voice can become the lower and vice versa, and the result still sounds correct.
Most invertible counterpoint is at the octave, where thirds and sixths simply trade places and stay consonant — the hazard there is the perfect fifth, which turns into a dissonant fourth, so use fifths only as passing or suspended dissonances. At the tenth, parallel thirds and sixths become octaves and fifths, so avoid them; at the twelfth, sixths become sevenths. Write both lines so that either could serve as the bass, and the passage works twice.
Bach's fugue countersubjects are written in invertible counterpoint — they work both above and below the subject, allowing endless recombination.
Invertible counterpoint is one of 1760 terms in the Gradus musical dictionary: the words, abbreviations and instrument names that appear in printed scores, plus the vocabulary composers use to talk about them.
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