How can I change the distance between text and underline in a WPF TextBlock?

Use element syntax to add an instance of TextDecoration to the TextBlock.TextDecorations, then you can adjust the Location or PenOffset.

<TextBlock>
    <TextBlock.TextDecorations>
        <TextDecoration Pen="..." Location="..."/>
    </TextBlock.TextDecorations>
</TextBlock>

(You may need to set the Pen via element syntax as well)