Eve is a simpler character than Adam. She is created from Adam's rib as his helpmeet. While she is beautiful, wise, and able, she is superior to Adam only in her beauty. From the time of her creation, when she looks in the water and falls in love with her own reflection, Eve is linked to the flaw of vanity, and Satan as the serpent will use this defect against her.
Before the fall, Eve is generally presented as submissive to Adam and, to some extent, dependent on him. Her reasoning powers are not as fully realized as his. However, Milton in no way suggests a lack of intelligence on Eve's part. Eve listens to Raphael's description of the war in Heaven and the defeat of the rebellious angels. When the conversation turns to more abstract questions of creation and planetary motion at the start of Book VIII, Eve walks away to tend her Garden. Milton is quick to note, however, "Yet went she not, as not with such discourse / Delighted, or not capable of her ear / Of what was high: such pleasures she reserv'd, / Adam relating, she sole Auditress" (VIII, 48-51). In other words, Eve is perfectly capable of comprehending the abstruse subject, but she prefers hearing the ideas from Adam alone. The implied idea here is that Eve understands her position in the hierarchical arrangement and leaves this conversation so that she will in no way usurp Adam's place with the angel.
Eve does have a tendency now and then to question Adam, but she does so in a rational, respectful manner. In Book IX, such questioning leads to temptation. Eve tell Adam at the start of Book IX that they can do more work if they work separately. Adam knows that Eve is more likely to be tricked by Satan if she is alone and argues against separation. His love for Eve, though, allows him to be persuaded, and against his better judgment, he lets her go. Most commentators see this action on Adam's part as another example of his uxoriousness; he yields to Eve's argument, not because her argument is better, but because he does not want to hurt her feelings. On the other hand, Eve wins the argument by knowingly using her advantages over Adam. Eve sets herself up for the fall and is not equal to the task of dealing with Satan by herself.
Eve yields to temptation through a combination of flattery (vanity) and sophistic argument by the serpent. Satan is happy to find Eve alone and acknowledges that Adam would be a much more difficult opponent. Satan knows Eve's weaknesses and plays on them. She is charmed by him and cannot detect the flaws in his arguments.
After she eats the fruit, Eve immediately changes. She begins to think of ways of becoming Adam's equal or perhaps his superior. But, fearful of losing Adam to another female creation, she decides that he must eat the fruit also. Adam does so but not because of Eve's arguments. He eats willfully because he is unwilling to be parted from Eve.
After the fall, Eve, like Adam, is acrimonious and depressed. However, her love for Adam initiates the regeneration of the pair. She apologizes, and her love causes a change in Adam; they can face the future together. Eve is also glorified by being told that her seed will eventually destroy Satan, though her position in relation to Adam is made clear when Michael puts her to sleep while he shows Adam the vision of the future.
Eve is certainly not a feminist heroine. Like so many characters in the epic, she has an assigned role in the hierarchy of the universe. Milton does not denigrate women through the character of Eve; he simply follows the thought of his time as to the role of women in society. Eve has as many important responsibilities as Adam, but in the hierarchy of the universe, she falls just below him.