Domain name is not Free exactly but it will costs you only $1. Hosting space will be absolutely free, if you already have a domain or you buy a domain name from DotEasy. The Unlimited Hosting plan of DotEasy will costs you $9.95/month normally but till October 27 2010 you can get this for free (1 year).
You will need a Credit card and they will charge you a nominal fee of 1.95$ , this amount you can use when you renew your account.(No PayPal accepted).
Read more about the hosting features
Read more and Sign up - (Buy a domain for $1 or transfer your existing domain) - but from next year onwards you will have to pay 25$ for domain registrations that is around 3 times what other domain register companies charge, But that includes a free basic hosting with the following features
Free with Domain Registration Purchase
No Ad Banner
100MB Free Web Hosting space
1GB Free Monthly Data Transfer
10 Email Accounts
Host 10 Add-On Domain
Free Website Creator
So better you think and decide on the domain name registering.
When you start registering and on the step where you choose the hosting plan choose "Unlimited Hosting plan", you can see a coupon code displayed enter it on the right side text box and click Add