Yes, and the legal footing here is not in your favor as much as you might expect.
You have the right to send mail. The facility has the right to reject it. Those two things can both be true at the same time, and in practice the facility's authority over what comes through their mailroom is broad and largely unreviewable from the outside.
When there are pending domestic charges in the picture, even ones you did not initiate, the facility treats that as a flag. Prosecutors and law enforcement routinely request that contact between a defendant and the alleged victim be restricted as a condition of pretrial detention, regardless of whether the alleged victim wants that restriction in place. A no-contact order can be put in place by the court without your input or consent. If one exists and the jail is aware of it, they are obligated to enforce it by blocking your mail, rejecting your calls, and preventing any contact from going through.
The first thing to determine is whether a no-contact order has actually been issued by the court. That information is part of the public court record for his case and can be checked through the North Carolina court system or by calling the courthouse clerk in the county where the charges were filed. If a no-contact order exists, it applies to both of you regardless of your wishes, and violating it from either end can create new legal problems.
If no such order exists and the jail is simply blocking your mail based on their own interpretation of the situation, that is harder to challenge but not impossible. His attorney is the right person to address this with, as they can communicate with the facility about what restrictions are actually in place and on what legal basis.
The system is not set up to accommodate what you want in this situation. Understanding exactly what orders exist is the necessary first step.