Answer
Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- There is no single rule that govern interaction between men and women in the Islamic sense. This is an area that is function of the situation and the nature of this interaction.
2- Any interaction between men and women has to be within a pure and decent atmosphere of politeness.
3- Lustful interaction, even only by way of looking or talking, is unacceptable in the Islamic code of morals.
Answering your question, Dr. Jasser Auda, a Professor and Al-Shatibi Chair of Maqasid Studies at the International Peace College South Africa, states:
There is no single rule that govern interaction between males and females in the Islamic sense. This is an area that is function of the situation and the nature of this interaction.
There is a newly-coined term that is quite popular these days, which is the term of ‘ikhtilat‘ (or ‘mixing’, i.e., of men and women). We all heard in the news the lashing of some people in some Muslim country for the crime of ‘mixing’, which is strange!
In the Islamic sources and scripts, there is nothing called ‘ikhtilat‘! The root of the word ‘ikhtilat‘ is never used in this context in the Islamic sources. It is used for ‘ikhtilat al-‘aql‘ (losing one’s mind), ‘ikhtilat al-mal‘ (trade partnership), and other meanings. But ikhtilat, the opposite of ‘segregation’ is not in the traditional Islamic language itself!
Interaction in the Quran
The Quran is full of incidences where men and women ‘mix’ and ‘interact’ in various ways.
The following are a few examples:
{And so she [Moses’ mother] said to his sister, “Follow him” – and [the girl] watched him from afar, while they [who had taken him in] were not aware of it. Now from the very beginning We caused him to refuse the breast of [Egyptian] nurses; and [when his sister came to know this,] she said: “Shall I guide you to a family that might rear him for you, and look after him with good will?”} (Al-Qasas 28:11-12
{Now when he [Moses] arrived at the wells of Madyan, he found there a large group of men who were watering [their herds and flocks]; and at some distance from them he came upon two women who were keeping back their flock. He asked [them]: “What is the matter with you?” They answered: “We cannot water [our animals] until the herdsmen drive [theirs] home – for [we are weak and] our father is a very old man.” So he watered [their flock] for them: and when he withdrew into the shade and prayed: “O my Sustainer! Verily, in dire need am I of any good which you may bestow upon me!”} (Al-Qasas 28:23-24)
{She [The Queen of Sheba] added: “O you nobles! Give me your opinion on the problem with which I am now faced; I would never make a [weighty] decision unless you are present with me.”} (An-Naml 27:32)
Interaction in the Sunnah
In fact, ‘mixing’ and ‘interaction’ happened everywhere during the time of the Prophet (peace be upon him); in the mosque, in the street, in the market, and everywhere.
The idea of ‘segregation of sexes‘ was simply not there! I will site a few hadiths below (out of thousands of similar narrations that you find in any hadith collection!) in order to make this point, without even needing to comment on them!
Qaylah al-Anmariyyah came to the Prophet and said: ‘O Messenger of God! I am a woman who buys and sells’. And then she asked about bargaining. (Ibn al-Atheer, Usd al-Ghabah, 5/535)
Anas ibn Malik narrated about the day of Uhud: I saw Aishah, the daughter of Abu Bakr, and Umm Sulaim rolling up their dresses, and I saw their leg-bangles, while they were carrying water skins on their back and emptying them in the mouths of the (wounded) people. They would return to refill them and again empty them in the mouths of the (wounded) people. (Al-Bukhari and Muslim)
Abu Usaid As-Sa`idi came and invited God’s Messenger on the occasion of his wedding. His wife, who was the bride, was serving them. Do you know what drink she prepared for God’s Messenger? She had soaked some dates in water in a Tur (is a vessel made of copper or stone) overnight. (Al-Bukhari)
The Prophet (peace be upon him) is reported to have said: “Don’t stop women form going to mosques at night”. A son of Abdullah bin Umar, on hearing this statement, said to his father: “We would not allow women to go out of the house at night for fear of any abuses”. Ibn Umar reprimanded his son: “I say the Prophet (peace he upon him) said so, and you still say you won’t allow it”. (Muslim)
Umar appointed Shifa bint Abdillah as the ameer (administrator) of the Market of Madinah which was the main market that existed in those days. (Ibn Hajar, Al-Isabah fi tamyyiz al-Sahabah, 4/333.)
Umar also appointed Samra bint Nuhayk as a muhtasibah (police officer). She carried a ‘whip to use in enforcing good and forbidding evil’. (Al-Tabarani).
Abu Hurairah reported: “The Prophet (peace be upon him) had just finished his prayer with us, when he directly turned and asked us to keep sitting, and then asked: ‘Is there amongst you any who would shut doors and draw curtains when he approaches his wife, but would later go out and tell everybody how he did so and so?’ All men present kept silent. Then the Prophet (peace be upon him) turned to the ladies and said: “Does any one of you openly discuss her conjugal matters with other women?” A young lady in the audience, when she heard this, knelt up on one knee and craned her neck so that the Prophet (peace be upon him) might see her and hear her speaking. She said: ‘Yes by God, all men discuss these matters among themselves and so do all women, too’. The Prophet (peace be upon him) said: ‘Do you know whom does one doing that compare to? Indeed it is like a satanic couple who meet on a high street and indulge their sexual desire in full view of the people'”. (Ahmad, Abu Dawud, and al-Bazzar)
Ibn Juraij reported that Abu al-Asba informed me that Jamilah, the singer, informed him that she asked Jabir bin Abdullah (a companion) about singing. So he replied, “Some Ansari married some relation of Aishah, so Aishah led the bridal procession. Then the Prophet (peace be upon him) said, have you presented your bride? She said, yes. He said: ‘Have you sent her off with singing for the Ansar love singing?’. She said, no. The Prophet said: ‘You should have sent for Arnab’ [a woman who used to sing in Madinah].” (Ibn Hajar, Al-Isabah fi Ma`rifat al-Sahabah, 8/4.)
A Decent Atmosphere
Having said that, one should know that this (natural) interaction has to be within a pure and decent atmosphere of politeness. ‘Lustful interaction’, even only by way of looking or talking, is unacceptable in the Islamic code of morals.
{Tell the believing men to lower their gaze and to be mindful of their chastity: this will be most conducive to their purity – [and,] verily, God is aware of all that they do. And tell the believing women to lower their gaze and to be mindful of their chastity, and not to display their charms [in public] beyond what may [decently] be apparent thereof.} (AN-Nur 24:30-31
This verse, as well as many of the specific rulings that scholars stipulate in men-women interaction, is meant to cut the roots of zina (adultery/fornication), which is a major sin in Islam.
Almighty Allah knows best.