Odysseus and Penelope from The Odyssey. Okay, there was the stuff with Circe and Calypso but neither of those was what you could call 100% consensual (because when a very powerful being that could kill you in a heartbeat wants to sleep with, you, it's smart not to argue, and Odysseus is nothing if not smart) and he did go to the ends of Earth (and Hell, and back) to get back to Penelope. That counts for something. As does the fact that he turned down immortality for her. For her part, Penelope did all she could to hold off the obnoxious suitors and stay faithful to her husband. After ten years of devotion to her husband, Penelope feared the worst and asked Artemis to strike her down painlessly, either because she wanted to be Together in Death with Odysseus, or because she knew her suitors would kill her son and force her to choose between them (or not even let her choose), or both.
Eros and his wife Psyche are an unlikely pair, considering how the vast majority of the Greek pantheon was constitutionally incapable of anything resembling fidelity. The story of the origins of their marriage is about trusting and going to great lengths to mend bridges.
The Rescue Romance of Perseus and Andromeda. Just the fact that neither cheated on the other is a very good sign.
Hilariously, TyphonandEchidna. Two of the worst monsters to ever come out of Tartarus (who by the by is their father), are entirely faithful to one another and support each other in all of their endeavours. Typhon eventually becomes Sealed Evil in a Can, but Echidna never moves on, and all of her young (and there are a lot of them) are also Typhon's. By Greek standards that is weirdly functional.
Hector and Andromache in The Iliad in sharp contrast to everyone else. Priam's a philandering bastard, Helen and Menelaus/Helen and Paris are horribly dysfunctional, and we won't even get started on Agamemnon and Clytemnestra. Hector and Andromache honestly seem to have been a good match.
Orpheus and Eurydice until she was dragged to Hades and even then, he loves her so much that he goes to Hades and back to try and get her back. And when he fails at the very last moment, man, how he mourns...
Hades and Persephone. The fact that he wanted to marry her (as in, keep her around) rather than have a one-night stand speaks volumes in Greek mythology. Hades's brothers Poseidon and Zeus (Zeus being Persephone's dad, even) were quite the philanderers. Hades was not.
Cyane and Anapos. Cyane tried to stop Hades from abducting/marrying Persephone by citing her own happy marriage as an example of consensual relationship, and as the opposite of Hades' own methods.
Ariadne and Dionysus. Dionysus saved Ariadne when she was left by Theseus on Naxos and she later accompanied him during his journeys. (Though some sources say that Dionysius had his eyes on Ariadne for a while already, and thus threatened Theseus in his dreams so he'd leave her.) He loved her enough to not only go down to the Underworld after her death to demand her soul back, but also made her immortal afterwards.
Pygmalion and Galatea. Specially noticeable in that Galatea originally was a sculpture made by Pygmalion, but she was brought to life and they got together.
Freyr and Gerðr, though getting her to fall for him leads to his death he didn't regret it.
Balder and Nanna. The Norse really liked their gods to be happily married before they were killed by giants.
Egyptian Mythology has Osiris and Isis who were surprisingly non-dysfunctional considering they were siblings. When the former was killed, the latter devoted much of her life to bringing him back.
Santa Claus and Mrs. Claus are usually portrayed this way, as part of the warm mythology of Christmas. (If Santa and Mrs. Claus didn't get along like the idealized grandpa and grandma, it wouldn't work with the rest of the story. This is extremely amusing for people who know that Santa Claus is based in part on the historical Saint Nicholas of Myra, who was a bishop and therefore celibate.)
Robin Hood and Maid Marian didn't get married in many of the original ballads (usually because she didn't exist yet), but many adaptations happily pair them off. The commentary for the 2010 movie stated that each era makes them into that era's idea of the perfect marriage.
Pwyll and Rhiannon from Mabinogion. They met and got married pretty quickly, but they had to deal with Rhiannon's jealous exboyfriend Gwawl who took advantage of Pwyll's kindness to demand to marry Rhiannon instead of Pwyll. Together they came up with a plan to get rid of Gwawl to get married. In their marriage, they have to deal with judgmental nobles because Rhiannon didn't get pregnant for the first two years of their marriage. When their son was conceived and born, they then lost himdue to their careless handmaids falling asleep. Worse, Rhiannon was framed by said handmaids who claimed that Rhiannon ate her son. Pwyll refused to set her aside and stays by her while she did her penance. The couple is eventually reunited with their son and now can properly named him Pryderi.