The Poet
Moore is as much a character as Adam and Eve, as she spends nearly 300 lines working through her feelings on marriage. She approaches the institution with alternating irony, derision, skepticism, curiosity, and frustration. She picks it apart and uses the works of others to present her multifarious views. She admits at the end that there can be rare unions that work, but most of the "savages" who try are deluding themselves.
Adam
A handsome but arrogant man, he gets away with things women cannot, has a much more vocal presence, and expresses his annoyance when Eve does not do what he thinks she should do. He is pleased that history has exonerated him, is proud to be an idol, and loves to hear the sound of his own voice. He "stumbles" over marriage and insults his wife, seeming only to value her for her beauty. His self-love blinds him to the nature of things.
Eve
Eve is a lovely and talented woman who falls in love with Adam in the heady days of the Garden, though she also values her solitary time. She is independent and has a high degree of self-love, which hurts her marriage. She is frustrated with how marriage has circumscribed her thoughts and movements and seems to resent Adam.