How to do it...

As we want to customize the template of the custom control to have a proper template binding, perform the following steps:

1. Open the Generic.xaml file, which is present under the Themes folder of the project.
2. Now, scroll down to the definition of the ControlTemplate as we need to customize the look and feel of it.
3. Search for the TextBox control named PART_TextBox, and set its Background, BorderBrush, BorderThickness, and Foreground properties to have a binding with the control's default properties.
4. Similarly, set the Background and Foreground property of the button (PART_Button) to the same properties of the control, by using template binding. Here's the complete code of the modified control template:

<ControlTemplate TargetType="{x:Type local:SearchControl}"> 
    <Grid> 
        <Grid.ColumnDefinitions> 
            <ColumnDefinition Width="*"/> 
            <ColumnDefinition Width="Auto"/> 
    ...