How to disable ScrollViewer in ListBox?

I have a ListBox. It has internal ScrollViewer, so I can scroll ListBox content with mouse wheel. It works fine until I set item template that contains another ListBox (in fact, I have 4 nested ListBoxes =)). Problem is that internal ListBox's ScrollViewer steals wheeling event. Is there any easy way to prevent this behavior?

I had ListBox with ItemContainerStyle like this:

<Style x:Key="ListBoxItemStyle" TargetType="{x:Type ListBoxItem}">
    <Setter Property="BorderBrush" Value="Black"/>
     ... 
</Style>
<ListBox ItemContainerStyle="{StaticResource ListBoxItemStyle}" />

How can I set style for ItemContainer's item border in resources like this? As I know ContentPresenter is item container of ItemsControl. But it hasn't Border, so I can't style it.