There is a reasonably prominent increase in density (and rigidity) of the inner and outer mitochondrial membranes where they are tethered to intermediate filaments tethered again with desmoplakin of the desmosome complex.  It occurs for the stretch which runs parallel to the desmosome and removed from it by about 140nm in height (as measured on these two micrographs – not ideal cross sections of desmosomes, so approximate dimensions).

Someone out there researching mitochondria membrane proteins probably knows which proteins these would be.  Top electron micrograph shows two separate mitochondria (tethered  — albeit tangentially) to the desomosomal complex showing intermediate filaments parallel to the plane of the plasmalemma in both instances. Red dot, ribosome=@27nm, red lines=intermediate filaments, blue curley brackets=inner mitochondrial membrane with increased density, green curley brackets=outer mitochondrial membrane with increased density at points of tethering. Dotted line in photo bottom left is where the outer mitochondrial membrane likely travels.