Database consistency after a power shortage

My question is regarding a potential situation:

I have a program that inserts values on 3 tables linked to each other. My
program is used in a POS. In this specific case, the program has to update
the tables "header_invoice", "detail_invoice" and
"payments_x_header_invoice".

In a normal operation, the program should insert first a registry on
"header_invoice", then insert N registries on "detail_invoice" referencing
the header_invoice number. After that it should insert N registries
regarding the payments related to the header_invoice, referencing again the
invoice.

So the order goes like this:
1) Insert 1 new registry on "header_invoice"
2) Insert N registries on "detail_invoice" referencing header_invoice
3) Insert N registries on "payments_x_header_invoice" referencing the
header_invoice

If lets say the header_invoice registry was inserted, operation was
committed and then a power shortage occurs and the system shuts down. In
that case the database will never know that more registries had to be
inserted, because that happened on the application level.

Is there any way to make the 3 operations be one transaction for the
database, so that it keeps them all consistent in case a power shortage
occurs in the middle?