How to get face from under overlay?

Here's the situation: I need to retrieve the face's under point boundaries, but if I use highlight-current-line mode, that face overlays the face that I'm interested in.

face-at-point or (get-char-property (point) 'face) will only give me the first face in the list, and it will be the one from the current-line overlay. How to get the underlying faces?

EDIT:

This is more or less what I ended up doing:

(defun haxe-face-at-point ()
  "This is like `face-at-point' except we will only look for faces
which are relevant to haxe-mode. This will also look under overlays
created by minor modes like ispel or highlight current line."
  (interactive)
  (let ((props (text-properties-at (point))))
    (catch 't
      (while props
        (when (eql (car props) 'face)
          (throw 't
                 (when (member (cadr props)
                               '(font-lock-string-face
                                 font-lock-keyword-face
                                 font-lock-variable-name-face
                                 font-lock-comment-face
                                 font-lock-preprocessor-face
                                 font-lock-type-face
                                 default))
                   (cadr props))))
        (setq props (cdr props))))))

I only needed to find out if there's one of the list anyways.

There are sadly no good facilities provided to Elisp code for that. The best I can offer you is to use overlays-at and then loop through the result, using overlay-get to see which ones of the overlays specifies a face and finally use get-text-property to get the face specified by the text-properties (if any). The display engine combines all those.