How to view and inspect a Commerce Billy invoice pdf template as HTML, before it's passed to the PDF generator?
If you check the page callback of PDF URL (i.e. "invoice-pdf/%commerce_order"), the HTML output of Invoice PDF is generated using commerce_billy_pdf_html($order) function. Same function is used by Print Invoice URL (i.e. "invoice-pdf/%commerce_order/print") to generate Printable output of Invoice. Since print page render HTML output you can inspect the output easily.

So for example, if your order number is 1 and your Invoice PDF URL is "invoice-pdf/1", then you can see the HTML Structure of PDF Output by going to "invoice-pdf/1/print" page.

Hope this helps.