Combo functionality on datagrid - wpf

I'm unable to get a combo to function as desired on a datagrid (using WPF).

A user should be able to select an item from a combo and the underlying database be updated when the user leaves the row.  The combo should look like a combobox and not like a textbox.

Desired view to the user (using seed data):

The combo looks like a combo.  

I could not get the underlying database updated so I posted this problem here and attempted what was suggested.  However, now I get a flat combo appearance which won't allow for selecting another item AND the underlying database is still not being updated.

After suggestion:

The combo functionality is lost.  Clicking on the cell does not allow for selecting another item.

Xaml (after suggestion):

<DataGridTemplateColumn Header="CPT Code" ><DataGridTemplateColumn.CellTemplate><DataTemplate><TextBlock Text="{Binding PartBBilling_CPT.PartBLookup_CPTCode}" /></DataTemplate></DataGridTemplateColumn.CellTemplate><DataGridTemplateColumn.CellEditingTemplate><DataTemplate><ComboBox ItemsSource="{Binding PartBCombo, 
                                      RelativeSource={RelativeSource AncestorType=Window}}" 
                                      DisplayMemberPath="PartBLookup_CPTCode" 
                                      SelectedItem="{Binding PartBBilling_CPT, UpdateSourceTrigger=PropertyChanged}"
                                      SelectionChanged="PartBCPT_SelectionChanged" /></DataTemplate></DataGridTemplateColumn.CellEditingTemplate></DataGridTemplateColumn>

SelectionChanged suggestion:

        Private Sub PartBCPT_SelectionChanged(sender As Object, e As SelectionChangedEventArgs)

            dgPartBBilling.CommitEdit(DataGridEditingUnit.Row, True)

        End Sub

What I would like is for the RowEditEnding event to fire to write the contents of the grid back to the database.

Thanks for any help or advice.

Thanks.