The answer for this questions is Yes and No. Confused? Let me explain.
BlueHost (and HostMonster and other web hosts) who claims to offer "FREE" unlimited domains means the ability to host unlimited domains without any extra charges. It does not include the domain registration fee which is around $10 to $15 depending on where you register it.
For example, if you own a condominium and the management provides you with "FREE" unlimited parking means they won't charge you for anything even if you park 2, 3 or 10 cars in their car park. But you still have to pay for the cars!
Before the era of multiple domain hosting which is started by BlueHost and HostGator a few years ago, hosting companies only allow you to host 1 domain per hosting account. If you owns several domain names, you will have to buy a new hosting account for each or pay an extra "parking fee" for each domain name!
In the condominium scenario, that would means you are only provided with 1 parking space and if you need more, you have to pay.
"Park as you like, but you still have to pay for the car dude."