They do complement one another, but it is far from an equal relationship. While portraying the two humans as created in the image of God, Milton is careful to stipulate that they are "Not equal, as their sex not equal seem'd." Adam is made for one purpose, Eve for another:
For contemplation hee and valour formd/For softness shee and sweet attractive Grace/Hee for God only, shee for God in him: [her looks implied] Subjection, but requir'd with gentle sway/And by her yielded, by him best receivd/ Yielded with coy submission, modest pride/ And sweet reluctant amorous delay.
Adam receives the gifts of reason and free will, and he is accountable only to God. Eve, on the other hand, must submit to Adam, to whom God has delegated absolute authority. In fact, we see later in the poem that the Fall occurs because Adam and Eve both fail to live up to their God-given roles: Eve does not obey God's commandment; Adam does not enforce it.
I will have to partially disagree with the first answer. This is because the relationship of superiority and inferiority actually varies and changes as the novel progresses.
Initially, Adam and Eve, when both are in the Garden of Eden, are initially equals. This is a standing fact from Books 1-9 (I believe). The complex of superiority is only brought up during Adam and Eve's first argument about Eve's capability of facing a trial of her virtue and resisting any temptations that would be set before her. This argument happens in Book 9 around lines 265-410 (I think. You'd have to read it for yourself to know the full passage, but I know for sure that it begins at Bk. 9 Ln. 265).
At line 271, Eve begins to be a tad sarcastic to Adam, as she not only did not expect for Adam to not have confidence in her, but that she was offended at Adam for having no confidence in her.
It is around line 291 that Adam attempts to inform Eve that it was not that he lacked confidence in her, but that they would have a better chance of fighting the temptation that Satan will present them with if they stick together. Between lines 301-315, Adam also states that when he is with her, he is more virtuous, implying even more of the fact that they need each other. However, instead of Eve taking this lightly, she, instead, becomes even more offended, bringing up the Great Chain of Being that is ever so implied in this novel (google or wiki it). In chronological order, just as God would come first in this chain, followed by spiritual/angelic beings, then humans (the link that ties the chain together), under them the bestial/bodily things, the chain begins to show up in this book with Adam and Eve, except, in this context, God would come first, followed by Adam, then Eve underneath.
Not to blabber on any more (going on the assumption that you read this poem), at around line 340, Adam states to Eve that because God has given him the proper reason (look up the Platonic Model of the Human Soul) and free will to choose what he wants to do, he must also give Eve this same choice as to whether or not she stays in one union as him (earlier in the novel, Milton implies that their first time having intercourse was when they became married) or to break away from him. Eve chose to leave. This whole passage alone proves that Milton had the intention of implying that Adam and Eve were equals, otherwise, he would have been fully capable of telling her that she was not allowed to leave, which would have been possible only if they were in a hierarchial relationship.
It is only until Book 10 when the relationship begins to show superiority vs. inferiority, as the Father sends the Son to see both Adam and Eve after the fall. In Bk. 10 line 130, the Son starts to hand out his punishment to Adam, Eve, and the snake (Satan). Around here, the Son gives Eve her punishments of a painful childbirth and patriarchy, meaning that she would now be subservient to man, or, in this case, Adam. Only here is when the superiority complex is installed within the relationship between Adam and Eve.