I've got a Datagrid with a column defined as this:

<Custom:DataGridTextColumn HeaderStyle="{StaticResource ComboBoxHeader}" Width="Auto" Header="Type" Binding="{Binding Path=Type}" IsReadOnly="True" />

The ComboBoxHeader style is defined in a resource dictionary as this:

<Style x:Key="ComboBoxHeader" TargetType="{x:Type my:DataGridColumnHeader}">
        <Setter Property="VerticalContentAlignment" Value="Center"/>
        <Setter Property="Template">
            <Setter.Value>
                <ControlTemplate TargetType="{x:Type my:DataGridColumnHeader}">
                    <ControlTemplate.Resources>
                        <Storyboard x:Key="ShowFilterControl">
                            <ObjectAnimationUsingKeyFrames BeginTime="00:00:00" Storyboard.TargetName="filterComboBox" Storyboard.TargetProperty="(UIElement.Visibility)">
                                <DiscreteObjectKeyFrame KeyTime="00:00:00" Value="{x:Static Visibility.Visible}"/>
                                <DiscreteObjectKeyFrame KeyTime="00:00:00.5000000" Value="{x:Static Visibility.Visible}"/>
                            </ObjectAnimationUsingKeyFrames>
                            <ColorAnimationUsingKeyFrames BeginTime="00:00:00" Storyboard.TargetName="filterComboBox" Storyboard.TargetProperty="(Panel.Background).(SolidColorBrush.Color)">
                                <SplineColorKeyFrame KeyTime="00:00:00" Value="Transparent"/>
                                <SplineColorKeyFrame KeyTime="00:00:00.5000000" Value="White"/>
                            </ColorAnimationUsingKeyFrames>
                        </Storyboard>
                        <Storyboard x:Key="HideFilterControl">
                            <ObjectAnimationUsingKeyFrames BeginTime="00:00:00" Storyboard.TargetName="filterComboBox" Storyboard.TargetProperty="(UIElement.Visibility)">
                                <DiscreteObjectKeyFrame KeyTime="00:00:00.4000000" Value="{x:Static Visibility.Collapsed}"/>
                            </ObjectAnimationUsingKeyFrames>
                            <ColorAnimationUsingKeyFrames BeginTime="00:00:00" Storyboard.TargetName="filterComboBox" Storyboard.TargetProperty="(UIElement.OpacityMask).(SolidColorBrush.Color)">
                                <SplineColorKeyFrame KeyTime="00:00:00" Value="Black"/>
                                <SplineColorKeyFrame KeyTime="00:00:00.4000000" Value="#00000000"/>
                            </ColorAnimationUsingKeyFrames>
                        </Storyboard>
                    </ControlTemplate.Resources>
                        <my:DataGridHeaderBorder x:Name="dataGridHeaderBorder" Margin="0" VerticalAlignment="Top" Height="31" IsClickable="{TemplateBinding CanUserSort}" IsHovered="{TemplateBinding IsMouseOver}" IsPressed="{TemplateBinding IsPressed}" SeparatorBrush="{TemplateBinding SeparatorBrush}" SeparatorVisibility="{TemplateBinding SeparatorVisibility}" SortDirection="{TemplateBinding SortDirection}" Background="{TemplateBinding Background}" BorderBrush="{TemplateBinding BorderBrush}" BorderThickness="{TemplateBinding BorderThickness}" Padding="{TemplateBinding Padding}" Grid.ColumnSpan="1">
                            <Grid x:Name="grid" Width="Auto" Height="Auto" RenderTransformOrigin="0.5,0.5">
                                <Grid.RenderTransform>
                                    <TransformGroup>
                                        <ScaleTransform/>
                                        <SkewTransform/>
                                        <RotateTransform/>
                                        <TranslateTransform/>
                                    </TransformGroup>
                                </Grid.RenderTransform>
                                <Grid.ColumnDefinitions>
                                    <ColumnDefinition Width="*"/>
                                </Grid.ColumnDefinitions>
                            <ContentPresenter x:Name="contentPresenter"
                                    HorizontalAlignment="{TemplateBinding HorizontalContentAlignment}" 
                                    VerticalAlignment="{TemplateBinding VerticalContentAlignment}" 
                                    SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}" 
                                    ContentStringFormat="{TemplateBinding ContentStringFormat}" 
                                    ContentTemplate="{TemplateBinding ContentTemplate}">
                                <ContentPresenter.Content>
                                        <MultiBinding Converter="{StaticResource headerConverter}">
                                            <MultiBinding.Bindings>
                                                <Binding ElementName="filterComboBox" Path="Text" />
                                                <Binding RelativeSource="{RelativeSource TemplatedParent}" Path="Content" />
                                            </MultiBinding.Bindings>
                                        </MultiBinding>
                                </ContentPresenter.Content>
                            </ContentPresenter>
                            <ComboBox ItemsSource="{Binding Path=Types}" x:Name="filterComboBox" VerticalAlignment="Center" HorizontalAlignment="Right" MinWidth="20" Height="Auto" OpacityMask="Black" Visibility="Collapsed" Text=""  Grid.Column="0" Grid.ColumnSpan="1"/>
                            </Grid>
                      </my:DataGridHeaderBorder>                      
                    <ControlTemplate.Triggers>
                        <Trigger Property="IsMouseOver" Value="True">
                            <Trigger.EnterActions>
                                <BeginStoryboard x:Name="ShowFilterControl_BeginStoryboard" Storyboard="{StaticResource ShowFilterControl}"/>
                                <StopStoryboard BeginStoryboardName="HideFilterControl_BeginShowFilterControl"/>
                            </Trigger.EnterActions>
                            <Trigger.ExitActions>
                                <BeginStoryboard x:Name="HideFilterControl_BeginShowFilterControl" Storyboard="{StaticResource HideFilterControl}"/>
                                <StopStoryboard BeginStoryboardName="ShowFilterControl_BeginStoryboard"/>
                            </Trigger.ExitActions>
                        </Trigger>
                    </ControlTemplate.Triggers>
                </ControlTemplate>
            </Setter.Value>
        </Setter>
  <Setter Property="Background">
      <Setter.Value>
       <LinearGradientBrush EndPoint="0.5,1" StartPoint="0.5,0">
        <GradientStop Color="#FF0067AD" Offset="1"/>
        <GradientStop Color="#FF003355" Offset="0.5"/>
        <GradientStop Color="#FF78A8C9" Offset="0"/>
       </LinearGradientBrush>
      </Setter.Value>
     </Setter>
     <Setter Property="Foreground" Value="White"/>
     <Setter Property="BorderBrush">
      <Setter.Value>
       <LinearGradientBrush EndPoint="0.5,1" StartPoint="0.5,0">
        <GradientStop Color="#D8000000" Offset="0.664"/>
        <GradientStop Color="#7F003355" Offset="1"/>
       </LinearGradientBrush>
      </Setter.Value>
     </Setter>
     <Setter Property="FontWeight" Value="Bold"/>
     <Setter Property="BorderThickness" Value="1,1,1,0"/>
     <Setter Property="HorizontalContentAlignment" Value="Center"/>
     <Setter Property="Padding" Value="5,0"/>
    </Style>

As you can see, I'm trying to databind the combobox's ItemsSource to Types, but this doesn't work. The list is in my ViewModel that is being applied to my page, how would I specify in this style that is in my resource dictionary that I want to bind to a source in my viewmodel.