Show this category's posts in menu

So I have a vertical UL menu which goes like this:

CATEGORY 1
CATEGORY 2
CATEGORY 3
CATEGORY 4
CATEGORY 5
CATEGORY 6

What I want is when you click a Category and go to a page, the Category Posts are listed in the menu as a sub list with different styling (and thus class) than the parent, like this:

CATEGORY 1
CATEGORY 2
Post 1
Post 2
Post 3
CATEGORY 3
CATEGORY 4
CATEGORY 5
CATEGORY 6

So in HTML my code would look something like this:

<ul class="parent">
  <li>CATEGORY 1</li>
  <li class="this_category">CATEGORY 2
     <ul class="child">
       <li>Post 1</li>
       <li>Post 2</li>
       <li>Post 3</li>
    </ul>
  <li>CATEGORY 3</li>
  <li>CATEGORY 4</li>
  <li>CATEGORY 5</li>
  <li>CATEGORY 6</li>
</ul>

I can not for the life of me figure out how to pull a list of “this category’s” Posts and insert them as a sub list in the menu though, nor can I find the answer even though I’m sure it’s out there.

Thanks.