I ran another test and unless I'm loosing my mind child categories are definitely displayed on the category archive page in WordPress v3.0.1 (is that the version you are running, or are you on an earlier version?)
Here are two screenshots, the first showing the category layout for my test install:
The next screenshots is the category archive page for my test install showing three posts, each with one category selected; the Parent, the Child and the Grandchild category, respectively.:
So I'm 95% certain you have a plugin or some other code that is disabling your subcategories from displaying on your archive page. Can you add the list of plugins you are using to your question content?