No it is not. If you have told him that you don't want him speaking to you that way, then of course it isn't right.
When he starts cursing at you, see if you can disengage and walk away. Don't participate in the "fight" if he is acting that way or when the fight is nonproductive.
Emotions can run high during verbal fights. Often, one or both partners say something they later regret. Is this part of a pattern? Do you feel you're in an equal relationship that is (outside of the arguments), respectful towards each other? What are the fights about? Is there a common theme? If so, can the problem that's causing tension be resolved in some way?
Like Kelly has suggested-When possible, I would walk away if he starts with the cursing. If it's an abusive situation however, where you're constantly having to 'walk on eggshells' for fear of upsetting him-well, that would be a different story and you should perhaps contemplate whether it's safe and healthy for you to remain in the relationship, long-term. Are children overhearing the cursing and nasty things? If so, both of you need to think about how that must feel for them: Seeing their parents 'at each other's throats.' Very upsetting and intimidating.
Clearly some boundaries need to be set (whether you have children or not).