Regarding roles, as was spelled out in the large post on the creation material earlier, both husband and wife are made in God's image. Both share in the commands to be fruitful and multiply, and fill the earth, and in dominion over the earth.
The same post spelled out indications of headship, even before sin. And the NT texts affirm headship.
In regards to the role of wife, both the text, and biology, indicate a nurturing role for the wife in the family, with a focus on the home, and children.
Titus 2:1-8
1 But as for you, speak the things which are proper for sound doctrine: 2 that the older men be sober, reverent, temperate, sound in faith, in love, in patience; 3 the older women likewise, that they be reverent in behavior, not slanderers, not given to much wine, teachers of good things— 4 that they admonish the young women to love their husbands, to love their children, 5 to be discreet, chaste, homemakers, good, obedient to their own husbands, that the word of God may not be blasphemed.
6 Likewise, exhort the young men to be sober-minded, 7 in all things showing yourself to be a pattern of good works; in doctrine showing integrity, reverence, incorruptibility, 8 sound speech that cannot be condemned, that one who is an opponent may be ashamed, having nothing evil to say of you. (NKJV)
1 Timothy 5:14
14 Therefore I desire that the younger widows marry, bear children, manage the house, give no opportunity to the adversary to speak reproachfully. (NKJV)
Psa 131:2 But I have calmed and quieted my soul, like a weaned child with its mother; like a weaned child is my soul within me
Isa 66:13 As one whom his mother comforts, so I will comfort you; you shall be comforted in Jerusalem.
Isa 49:15 “Can a woman forget her nursing child, that she should have no compassion on the son of her womb? Even these may forget, yet I will not forget you.
1Th_2:7 But we were gentle among you, like a nursing mother taking care of her own children.
The curse related to Eve, following transgression also relates to this role of the wife, in bearing children. This role was already defined, as part of the command to be fruitful and multiply, but now would be more difficult due to sin.
Genesis 3:16
16 To the woman He said:
“I will greatly multiply your sorrow and your conception;
In pain you shall bring forth children;
Your desire shall be for your husband,
And he shall rule over you.” (NKJV)
That is not to say that women did not do other work, besides that related to children and the home. We see descriptions of such work as well, for instance in Proverbs 31:
Proverbs 31:13-28
13 She seeks wool and flax,
And willingly works with her hands.
14 She is like the merchant ships,
She brings her food from afar.
15 She also rises while it is yet night,
And provides food for her household,
And a portion for her maidservants.
16 She considers a field and buys it;
From her profits she plants a vineyard.
17 She girds herself with strength,
And strengthens her arms.
18 She perceives that her merchandise is good,
And her lamp does not go out by night.
19 She stretches out her hands to the distaff,
And her hand holds the spindle.
20 She extends her hand to the poor,
Yes, she reaches out her hands to the needy.
21 She is not afraid of snow for her household,
For all her household is clothed with scarlet.
22 She makes tapestry for herself;
Her clothing is fine linen and purple.
23 Her husband is known in the gates,
When he sits among the elders of the land.
24 She makes linen garments and sells them,
And supplies sashes for the merchants.
25 Strength and honor are her clothing;
She shall rejoice in time to come.
26 She opens her mouth with wisdom,
And on her tongue is the law of kindness.
27 She watches over the ways of her household,
And does not eat the bread of idleness.
28 Her children rise up and call her blessed;
Her husband also, and he praises her: (NKJV)
Moreover, just as the role of children changes over time, so the role of a wife changes over time. This emphasis on nurturing of children is no longer as prominent for the older women, who take on more of a teaching role for the younger women, etc. per the text above in Titus.
We also see that those such as Lydia engaged in their own business. As she appears to have been unmarried, and is said to be the head of her own household, she would obviously have different roles, with no husband, or children, etc., but is still seen to be serving the Lord.
I Corinthians 7 speaks about those who have a gift to remain unmarried, and who can focus on pleasing the Lord.
But the text also indicates that one has one gift, one the other, and most are called to the vocation of marriage and family.
Both husband and wife are involved with disciplining children, and children are commanded to obey both.
Husbands in particular are encouraged to discipline, and held to account for the manner of discipline:
1Sa 3:12 On that day I will fulfill against Eli all that I have spoken concerning his house, from beginning to end.
1Sa 3:13 And I declare to him that I am about to punish his house forever, for the iniquity that he knew, because his sons were blaspheming God, and he did not restrain them.
(as was noted, this involves multiple roles, with high priest and father, but the father aspect is emphasized in this text).
Pro 13:24 Whoever spares the rod hates his son, but he who loves him is diligent to discipline him.
Psa 103:13 As a father shows compassion to his children, so the LORD shows compassion to those who fear him.
Col 3:21 Fathers, do not provoke your children, lest they become discouraged.
Eph 6:4 Fathers, do not provoke your children to anger, but bring them up in the discipline and instruction of the Lord.
Heb 2:9 Besides this, we have had earthly fathers who disciplined us and we respected them. Shall we not much more be subject to the Father of spirits and live?
Th 2:11 For you know how, like a father with his children,
1Th 2:12 we exhorted each one of you and encouraged you and charged you to walk in a manner worthy of God, who calls you into his own kingdom and glory.
We see texts speaking of the father setting the tone for the whole family.
Jos 24:15 And if it is evil in your eyes to serve the LORD, choose this day whom you will serve, whether the gods your fathers served in the region beyond the River, or the gods of the Amorites in whose land you dwell. But as for me and my house, we will serve the LORD.”
Jer 35:18 But to the house of the Rechabites Jeremiah said, “Thus says the LORD of hosts, the God of Israel: Because you have obeyed the command of Jonadab your father and kept all his precepts and done all that he commanded you,
Jer 35:19 therefore thus says the LORD of hosts, the God of Israel: Jonadab the son of Rechab shall never lack a man to stand before me.”
Acts 10:1-2
1 There was a certain man in Caesarea called Cornelius, a centurion of what was called the Italian Regiment, 2 a devout man and one who feared God with all his household, who gave alms generously to the people, and prayed to God always (NKJV)
Acts 18:8
8 Then Crispus, the ruler of the synagogue, believed on the Lord with all his household. And many of the Corinthians, hearing, believed and were baptized. (NKJV)
1 Timothy 3:2-5
2 A bishop then must be blameless, the husband of one wife, temperate, sober-minded, of good behavior, hospitable, able to teach; 3 not given to wine, not violent, not greedy for money, but gentle, not quarrelsome, not covetous; 4 one who rules his own house well, having his children in submission with all reverence 5 (for if a man does not know how to rule his own house, how will he take care of the church of God?) (NKJV)
The exception seems to be those households where single women head the household, and have a similar role in setting the tone.
Acts 16:14-15
14 Now a certain woman named Lydia heard us. She was a seller of purple from the city of Thyatira, who worshiped God. The Lord opened her heart to heed the things spoken by Paul. 15 And when she and her household were baptized, she begged us, saying, “If you have judged me to be faithful to the Lord, come to my house and stay.” So she persuaded us. (NKJV)