You can get one or the other but not both. Free web hosting sure no problem their are several companies that are more than happy to give this to you.
Free domain, no problem many hosting companies will give you a free domain as long as you purchase hosting from them. I do not know of any resource that will give you a completely free domain name. If that were the case then GoDaddy would have been out of business. Bottom line is that these companies will get something in return. Its just Business.
