What is the difference between the measure words 面 vs 张 Apparently both are measure words for flat objects, are they interchangeable or is there a difference to the types of flat objects they are used for?
张 (zhang1) is used for different objects, that may or may not be related with each other, e.g. sheets and flat furniture. If we really want to find a common denominator, I think that would be objects that are spread open [1]:


纸 paper (一张纸 a sheet of paper)
地图 map
照片 photo, picture
桌子 table
床 bed
木板 plank
脸 face （一张脸）
嘴 mouth （一张嘴）
弓 (gong1) bow （一张弓）




面 (mian4) is used for flat objects with a face or a surface:


镜子 mirror
旗子 flag
墙、墙壁 wall
鼓 drum
锣 （luo2) gong
盾 (dun4) shield



[1] that's not a dictionary definition. It's personal advice that hopefully makes enough sense to you to work as a reasonable rule of thumb.