It is important to remember that because of the nature of the story that Milton writes about, any characteristics or roles that Adam and Eve assume are considered to be natural rather than something that is forced upon them by society. By going back to the very beginning of the human species, Milton is therefore trying to present an authoritative treatment of gender and gender roles that is uninfluenced by society at large, as there was no society to influence the development of Adam and Eve. Milton's presentation of the creation of Adam and Eve and their first actions include vital hints at how he sees their role in society.
For example, in Book IV, Eve describes how she saw her own reflection and became enchanted by it, "pinned with vain desire":
A shape within the watery gleam appeared
Bending to look on me, I started back,
It started back, but pleased I soon returned,
Pleased it returned as soon with answering looks
Of sympathy and love...
Eve, from the moment of her creation, is presented as a creature of vanity, who is aware of her appearance and is caught up with her own self-obsession. Adam, by contrast, is presented in a very different way. From his own account of his birth in Book VIII, he was not obsessed with vanity in the same way:
Straight toward heaven my wondering eyes I turned,
And gazed awhile the ample sky, till raised
By quick instinctive motion up I sprung,
As thitherward endevouring, and upright
Stood on my feet...
Adam immediately recognises God and seeks him through his gaze before seeking to follow with the rest of his body. He is naturally inquisitive and forceful in the way he stands and takes stock of his surroundings. This of course links with the way that Adam takes a protector role in the epic, seeking to look after Eve, who is viewed as the "lesser" and weaker of the two sexes.