Paint problems when parent, child on different threads

[IntelliSteve]

I've run into a situation where my application (through no fault of its own)
has the following:

Parent Window hParent and ChildWindow hChild are on different threads.
(Basically, someone calls into my app to create a window and provides a
parent whose message pump is running on another thread.)

In this scenario, sporadic painting problems occur. When the client area of
the parent window (and the child window in question) is off-screen, and you
drag the window back on screen (filled drag is on, of course), there are
occasional failures to paint in the child's client area.

What is seen is that the parts that fail to paint have been erased using the
child window's brush.

And to make it even more fun, attempting to spy on the messages scares the
bug away. Dumping debug strings hasn't proved very helpful, either.

Anyone out there encountered similar problems?