The key to gender interaction (aka gender relations) is professionalism.
During the lifetime of the Prophet, peace be upon him, ‘Umar said to one woman sahaba in Abysinnia: “We have more right to the Prophet then you”. She said (to the effect of) “nope”. She approached the Prophet and narrated the incident to him, and he said “‘Umar was incorrect. You (Abyssinians) made hijrah (migration) twice, you get double the reward.”
This hadith was more beloved to them then the dunya and everything in it.
The companion spread it far and wide, and taught it to several people, both men and women. If you investigate the event, and other similar events, you will see the companions treated each other, in terms of gender interaction, with professionalism. Never will you see joking around.
This is the key to gender interaction. Keep it professional, purposeful, and limited. Wallahu ‘alim.
Imam Anwar al-Awlaki. Life in Mecca.