I have to give a partial answer because this is too complicated to figure out on the spot and I already blew my time budget.
Face is a frame property. A frame can display multiple buffers at the same time. Mode is a buffer property. You ask how to vary the face on a per-mode basis. Combining all this, it seems that the question cannot not have a single fully-correct answer.
You can approximate the desired answer if you assume that a given frame will never display more than one buffer. You can actually accomplish that with something like this, but modified to use special-display-regexps and a set of regexps that match your markdown-mode buffer names.
(append special-display-buffer-names
'("*VC-log*"
"*Help*"
("*Completions*"
(height . 25)
(font . "8x13"))))
However, this is probably not what you want. Your question seems to imply changing the face properties of a single frame.
Again assuming that a frame will never display more than one buffer at a time, you can try advising switch-to-buffer. But that might not be sufficiently low level and it might be too slow. (untested)
(defadvice switch-to-buffer (after switch-to-buffer activate compile)
"change the frame's default face after switch-to-buffer"
(doSomethingToChangePropertiesOfDefaultFace))
And now for my actual (incomplete) answer...
A better, albeit more complicated, approach would instruct markdown-mode to use a new face for all regions that are not already assigned one of the built-in faces. You can create a new face with copy-face and give it interesting properties with set-face-*.
Modify markdown-mode's font-lock-defaults to override the default font-lock-fontify-region-function as described in the comment block near line 946 of font-lock.el that begins, "Fontification functions". You can probably use a very slightly modified font-lock-default-fontify-region that does just one extra step immediately after it does:
(unless font-lock-keywords-only
(font-lock-fontify-syntactically-region beg end loudly))
The extra step parses the region similar to what font-lock-fontify-syntactically-region does, breaking the region into "interesting" sub-regions. But this time you find sub-regions that have the default face and you put-text-property those sub-regions to the new face that you previously created.
In all this feels like it should be only a couple lines of elisp in your .emacs file, plus make a copy of font-lock-default-fontify-region that has only a minor diff from the original (call one new function), plus make a copy of font-lock-fontify-syntactically-region and modify it to do your bidding (the most difficult part).
Actually, if you "after" advise font-lock-fontify-syntactically-region then you probably don't even need to modify font-lock-defaults or font-lock-default-fontify-region.