Parent Child Relationships With DIVs

I am seeking guidance on what seems like it's a browser bug, but is
displayed across many browsers:

I have created a dropdown menu using a DIV that contains a UL, which has
several LI contained within.  The DIV display is set to 'none' until someone
MouseOvers an image.  On the MouseOver I set the DIV's display to 'block'.
However, if set the DIV's display back to 'none' on the DIV's MouseOut
event, the minute it encounters the UL, it fires the MouseOut and the DIV
vanishes.

If I set the MouseOver of the UL to set the DIV's display to 'block', and
then MouseOver the LI, the DIV stays shown until I leave the UL.

Now it seems that even though the DIV is parent to the UL element, no
connection is maintained across events between them.
But with parent-child relationship between a UL and an LI, it maintains the
parent-child relationship across events.

My question is this:
Are both of these behaviors correct?  Should the Parent-Child relationship
be maintained across all of the DIV's children between events, so that if
you are mousing over the UL (or any other HTML element.  This behavior is
exhibited with A tags or TABLE, etc.  UL just happened to be what I used)
which is a child of the DIV, it counts also as a MouseOver of the DIV?  Or
should the currently maintained relationship between the UL and it's
children LI be severed?

Thanks in advance,
Maurice Reeves