<DataTemplate x:Key="postBody" TargetType="{x:Type Post}">
  <Grid>
    <TextBlock Text="{Binding Path=author}"/>
    <Button Click="btnDelete_Click" Content="Delete"/>
  </Grid>
</DataTemplate>
<ListBox ItemTemplate="{StaticResource postBody}" ItemSource="{Binding Posts}"/>

Code behind to get a reference to object owning btnDelete:

private void btnDelete_Click(object sender, RoutedEventArgs e)
{
  var post = ((Button)sender).DataContext as Post;
  if (post == null)
  {
    throw new InvalidOperationException("Invalid DataContext");
  }
 
  Console.WriteLine(post.author);
}