House account invoices can be emailed along with statements.

When selecting email statements in a house account profile, you can check the box to enable sending invoices. The email sent will have two files attached, one for statements and one for invoices.

To send invoices from a house account, go to Reports > House Accounts and select the customer, then click Email Statement. 

Make sure the customer's email is listed and check the Include Invoices box, then click Send Email.