Debit Cards are processed as "Credit Cards" through whatever merchant the card is issued through (Visa, Mastercard, etc). When a seller processes a card online, it doesn't care whether it's a "credit" card, or a debit card. It only cares that the merchant approves the transaction, and releases the funds.
So the short answer is, yes, you can use your debit card as a credit card.
I know for a fact I can't use my debit card as a credit card... Maybe it's different in other countries / banks?