Penelope is often held up as a prototype on an ideal Greek woman. She is loyal to her husband, a good mother to her son, steadfast, determined, and extremely clever. Although she is a far stronger woman than is ordinarily held up as a role model in ancient epic, she is also clearly subordinate to her husband and undermines male authority only in service of son and husband, and thus does not violate gender norms. Her main stratagem involves weaving, which was an important task for women in antiquity and central to the domestic economy. Weaving a burial shroud is also a sign of her being a virtuous woman as funerary rites were a female duty in this period. The main element of Penelope's relationship to Odysseus is loyalty, even to the point of refusing to believe he has died and enduring much to preserve her self and Ithaca for his return.
Odysseus also is loyal to Penelope but is less consistent in his loyalty. In Homer's time, his sleeping with other women would not have been considered problematic but the extensive delays in his journey appear somewhat irresponsible.
In the reunion after Odysseus returns, both characters test each other. Once they are assured of each others' loyalty and identity they work together, displaying mutual trust and support. Although the relationship is clearly a strong and loving one, both characters are clever and have wills and minds of their own, making them a good match for one another.
Penelope and Odysseus love each other. Though they are separated for twenty years, they remain focused on reuniting. Odysseus uses his wits to get home to Penelope, and Penelope uses her wits to avoid marrying any of the many suitors who hope to take Odysseus's place.
Penelope is the emblem of the faithful wife. She never gives up on Odysseus and never is disloyal to him. Even when he returns, she tests him to make sure he really is her husband. Because of the double standard concerning sexual faithfulness, Odysseus does sleep with other women during his time away, but his heart is always with Penelope. He withstands marriage offers from other women, determined to get back to his beloved wife.
Penelope and Odysseus are both sensitive people who feel deeply. Although a mighty warrior, Odysseus is able to cry in grief over a song about the Trojan war. Penelope cries often over her missing husband and grieves deeply for him. The couple is well-matched: not only are they both feeling people, they are both strong, intelligent, wily, resilient, and faithful.
The relationship between Odysseus and Penelope both reflects and, at the same time, transcends the cultural norms of the time. They are king and queen of Ithaca and have a very strong sense of regal duty. With Odysseus absent on his various adventures, Penelope needs to hold the fort, as it were, keeping her husband's kingdom intact while the royal palace is besieged by suitors claiming her hand in marriage.
But Odysseus and Penelope are held together by more than just the bonds of duty. They feel a deep sense of love and loyalty to each other, a sense strengthened by their long separation. They both embark upon journeys of their own, voyages of discovery in which they don't just find themselves but also gain a deeper understanding and appreciation of their marriage and its loving foundation. At every stage of their respective odysseys they are both always working their way back to each other, using their immense courage, intelligence, and ingenuity to remove the myriad barriers that have separated them for so long.
I concur with Jdslinky, the relationship between Odysseus and his wife Penelope is anchored in love and loyalty. The couple goes through an extremely tough period when Odysseus’ journey back home from Troy is interrupted by significant delays. During that period, their relationship is put to the test, but eventually, the couple overcomes and the two are happily reunited.
There are a number of examples that show the strong marital values held by Odysseus and Penelope. Starting with Penelope, she fended off advances from the pesky suitors who were bent on marrying her. She was forced to employ her wit in order to buy some time, hoping that her husband would return. Penelope did not fall into temptation like Agamemnon’s wife, who together with her lover arranged the murder of her husband. On the other hand, Odysseus declined to marry Calypso and the goddess Circe both who took good care of him. Odysseus returned to his wife as promised despite overtures made by Circe and Calypso.
The relationship between Odysseus and his wife Penelope is one of loyalty, love, and faith. Both characters are driven by these characteristics.
Odysseus displays his loyalty in his constant battle to get home to his wife. The entire journey consists of his reaction to one confrontation after another, including marriage offers and the promise of immortality from those who meet and fall in love with him (i.e. Nausicaa and Calypso). Penelope's loyalty is unwavering as she patiently waits for him while raising their son, all the while remaining faithful to him and refusing to take a suitor.
The love they share across the miles and over the years is a withstanding one-it sustains them both, as does the promise that they will be reunited. Their faith in the strength their marriage was built upon gets them through the most difficult parts of the journey/wait.