Even so, each host who claims unlimited will stop you at some point when you use to much. It would be better if they give you the limit they will allow you get up to as then you will know how close you are to that limit.
I am not saying they will but this host could kick you off for using 5gb of bandwidth. On the other hand they might allow you use 100gb. To alot of hosts both of these are acceptable but to some that offer "unlimited" will kick you off before these limits. Bluehost is a good example of that. Unlimited disk space and bandwidth but really low CPU limit so you will get kicked of using to much cpu but because the limit is so low you will only be using 20gb bandwidth.