Why do mitochondria have a phospholipid bilayer?
I think the question is based on a false premise:


  Poster: Now, mitochondria are said to have been archaea, right? 
  
  Me: Wrong, I’m afraid.


The closest bacterial relation of mitochondria is  Rickettsia, an alpha-Proteobacterium (see Lang et al. for a review). Rickettsia is a eubacterium, not an archaebacterium.

The confusion is probably due to misreading one of the two alternative theories of the origin of mitochondria. This is the theory that the host for the original mitochondrion was an archaebacterium (rather than a primitive nucleated eukaryote). In both theories this host aquired a eubacterium related to Rickettsia, which gave rise to the mitochondrion.