What is the part of speech of the underlined phrase in the sentence below? Is the jacket on the couch yours or mine? on the couch is underlined

A phrase consisting of multiple words cannot have a single part of speech - part of speech refers to singular words in isolation. If you mean what the function of on the couch is, then the answer is - adverb phrase. If, however, you really do need a part of speech, then you have to do it word by word: on is a preposition, the is a determiner, and couch is a noun.