Hubspot API to create a form submission (not an Hubspot form)

[sfflor]

We are using a form on our website to retrieve information from customers, but this needs to be stored in our website (for billing and syndication) but also needs to be integrated with HubSpot for marketing and CRM purposes.
As a part of this integration through the HubSpot API we are able to create a contact but we are not able to simulate a form submission, with all the fields we need and then to integrate with our CRM.
Can we make the same events happen as a form submission while using Hubspot API?

[3PETE]

@sfflor can you send the data to HubSpot and to your billing system at the same time upon submission?