the inner/outer membranes, and intermembrane space

• the outer membrane:

  The phospholipid composition of the outer membrane is similar to that of the membrane around other organelles in eukaryotic cells. it contains proteins, some of which form channels or carriers, that allow the passage of molecules like pyruvate into the mitochondrion
• The inner membrane:

  The lipid composition of the inner membrane differs from that of the outer membrane, this lipid membrane is less permeable to small molecules like protons than is the outer membrane. the cristae in the inner membrane give a large surgace area for the surface electron carriers and ATP synthase enzymes embedded inside of them. The electron carriers are protein complexes arranged in electron transfer chains. ETCs are involved in the final stages of aerobic respiration's oxidative phosphorylation.
• The intermembrane space:

  The intermembrane space between the outer/inner layers of the mitochondrial envelope is also involved in oxidative phosphorylation. the inner membrane is in close contact with the mitochondrial matrix, so the molecules of reduced NAD and FAD can easily deliver hydrogens to the electron transport chain.