Recourse if debit card was used on a suspicious website

Don't report this as fraud; that will kick off an investigation that will ultimately conclude you did authorize the transaction. Waste of time all around.

• Call the card company, tell them you made a purchase on a site that is not at all PCI-compliant, is "likely fraudulent" and your card information is now assumed compromised.
• Go through the hoops to get a new card issued with new numbers.
• Wait 30-45 days to see if the glasses show up. Be pleasantly surprised if they do. If they don't, dispute the charge before the end of the dispute period (gen. 60 days).
• Educate your husband to never buy anything marketed through ads. Even when the goods are delivered, they're seldom as good a deal as you think.

As for identity fraud, I'm not seeing birthdays or socials in the form, so it's unlikely they could actually do anything with it. They ask for enough information to authorize a transaction so I'd expect fraudulent charges on the card at worst if you don't shut it down immediately.

The best course of action would be to contact your card provider and ask to block the transaction. Also, I recommend you block your credit card number and get a new replacement credit card. Here's why:

The whois information for the website reveals that it is registered to someone in China with most likely a fake address:

Domain Name: RBXZO.COM 
Registry Domain ID: 2137576384_DOMAIN_COM-VRSN 
Registrar WHOIS Server: whois.publicdomainregistry.com 
Registrar URL: www.publicdomainregistry.com 
Updated Date: 2017-06-27T10:21:01Z 
Creation Date: 2017-06-27T10:21:00Z 
Registrar Registration Expiration Date: 2018-06-27T10:21:00Z 
Registrar: PDR Ltd. d/b/a PublicDomainRegistry.com 
Registrar IANA ID: 303 
Domain Status: clientTransferProhibited https://icann.org/epp#clientTransferProhibited 
Registry Registrant ID: Not Available From Registry 
Registrant Name: liu fuquan 
Registrant Organization: liu fuquan 
Registrant Street: guangdongsheng zhaoqingshidinghuqu    
Registrant City: BeiJin 
Registrant State/Province: BeiJin 
Registrant Postal Code: 526000 
Registrant Country: CN 
Registrant Phone: +86.017082434147 
Registrant Phone Ext:  
Registrant Fax: +86.017082434147 
Registrant Fax Ext:  
Registrant Email:

The registered email at qq.com also looks fake.

The website itself asks to register an account and set password on a non-SSL (not properly secured / no encryption) HTTP page as seen below:

I did not actually go through with the registration page and cannot see the payment page, but I doubt that they have HTTPS (SSL) encryption on there either.

Overall, very shady and I highly recommend you block the transaction, the credit card and get a new credit card delivered to you.

Addendum:

• As someone pointed out in comments, the password your husband created or used on the website should not be used elsewhere anymore. If your husband has that same password set elsewhere, we recommend changing it.
• Also, to clarify, you can try to cancel the transaction, but as others pointed out, you did initiate the transaction and so it's a valid transfer of money as far as your financial institution is concerned. So you will likely not recover the money your husband spent on the website. But you can block the card and ask for a new one to prevent misuse of your card in the future.

Looks exceptionally scammy to me I'm afraid.. I would contact the issuer of the credit/debit card ASAP and go from there. Odds are pretty good that you'll be able to get the money back - most likely outcome is cancelling and re-issuing the card but you'll have to go through every transaction on that card with a fine tooth comb for any time period between placing that order and getting the card cancelled.