If I have this straight, you want a control that has something arbitrary displayed along with a drop-down button that displays a list of items with checkboxes next to them?
I wouldn't even bother trying to restyle a ComboBox to achieve this. The problem is that ComboBox is more specialized down a different path than what you need. If you look at the ComboBox ControlTemplate Example, you'll see that it simply uses a Popup control to display the list of possible values.
You can take pieces of that template as guidance to creating a UserControl that is easier to understand and better provides what you want. You'll even be able to add a SelectedItems property and such that ComboBox doesn't provide.
An example of what I mean by guidance: the Popup has an IsOpen property. In the control template, it's set to {TemplateBinding IsDropDownOpen}, which means that the ComboBox class has an IsDropDownOpen property that is changed in order to control the expand/collapse of the Popup.