This is an interesting question and, in answering it, it must be recognized that Milton introduced some of the social biases of his period into his descriptions of Adam and Eve, their relationship and what they want from each other. It must be recognized that these social biases no longer apply in our society and that they have been thoroughly rejected and substantially refuted. In other words, Milton's depiction of men and women, through representative Adam and Eve, is not a universal depiction; it is a socially contextual depiction and it is one that is no longer held as valid.
One thing that Milton shows Adam wants from Eve is a reasonable mind that is capable of reasoned, rational thought. It is Reason that allows for and governs, first, self-knowledge and, then, self-rule. It is Reason, moreover, that allows knowledge of God. Adam instructs Eve in the role of Reason and this is what he wants from her:
... we live
Law to ourselves, our Reason is our Law
On thing Milton shows that Eve wants from Adam is the recognition of her being independent and strong. After Satan appears to Eve through the dream that he induces while in the form of a frog, Eve requests that she and Adam work separately to be more productive in their garden. Adam hesitates because of the enemy Raphael has warned him about. Eve insists because she wants Adam to see her as independent and strong, not dependent and weak. Adam gives in against his will though he feels she will come to harm.
[This scenario is a representation of the social bias against women's capabilities during Milton's era.] And come to harm is precisely what befalls Eve. Because she can't claim Reason, self-knowledge and self-rule, she is led into folly and that folly results in the Fall from Paradise.
Firm we subsist, yet possible to swerve
Since Reason not impossible may meet
And fall into deception unaware.