Two-way binding doesn't work with ComboBox.Text?

I have a style:
<Style x:Key="JournalInput"
TargetType="{x:Type ComboBox}">
<Setter Property="Template">
<Setter.Value>
<ControlTemplate>
<TextBox Text="{Binding
RelativeSource={RelativeSource TemplatedParent}, Path=Text, Mode=TwoWay}"/>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>

If I have a combo box:
<ComboBox Name="MyCombo" Text="StartText" KeyDown="HandleKeyDown"/>

The binding will work to the point that the textbox contains "StartText",
but if I break in HandleKeyDown where e.Key == Key.Enter after entering, for
example, "XYZ", MyCombo.Text still equals "StartText". Am I mishandling the
binding somehow? According to the documentation, it should be binding 2-way
by default.