一面 … ，一面 … (two things at once)

Driving and chatting

• Your uncle is a taxi driver who loves to tell stories while he drives.
• he他tāwhile一面yí miànto drive a car开车kāi chē，while一面yí miànwith / and跟gēnpassenger乘客chéng kèto chat聊天liáo tiān。 — "He chats with passengers while he drives."

while一面yí miàn A，while一面yí miàn B = doing A while doing B

• while一面yí miàn A，while一面yí miàn B = two actions at the same time by the same person, like while一边yì biān…while一边yì biān….
• It is a little more formal and written.

she她tāwhile一面yí miànworking工作gōng zuò，(at the same time)一面yí miànstudying读dúfor a master's研究生yán jiū shēng。

Ongoing parallel activities

• Can describe long-term parallel activities: he他tāwhile一面yí miànattending上shànguniversity大学dà xué，while一面yí miànworks part-time打工dǎ gōng。 — "He goes to university and works part-time."
• Also for two attitudes: while一面yí miànto criticize批评pī píng，while一面yí miànto encourage鼓励gǔ lì — "criticising and encouraging at once."

he他tāwhile一面yí miànattending上shànguniversity大学dà xué，(also)一面yí miànworks part-time打工dǎ gōng。

Same subject, actions

while一面yí miàn versus while一边yì biān and on the one hand一方面yì fāng miàn

• while一边yì biān…while一边yì biān… is the everyday version: while一边yì biānvariant of 吃吃chīwhile一边yì biānwatches看kàn.
• on the one hand一方面yì fāng miàn…on the one hand一方面yì fāng miàn… gives two aspects or reasons, not two simultaneous actions.

he他tāwhile一边yì biāneating吃饭chī fàn(also)一边yì biānwatches看kànthe news新闻xīn wén。

Recap

Read the full reference: HSK 5 grammar — Sentence patterns.