According to the New York State DMV, if a driver is convicted of a violation where a passenger under age 16 is not wearing a seat belt or in a child safety seat, 3 points are assigned to the driver's record. If instead you are convicted of a seat belt violation just involving the driver or a passenger age 16 or older, no points are assigned to the driver's record.
If your husband is assessed points then the points will be counted from the date of the traffic violation, not from the date of his traffic conviction. A traffic conviction is required for the points to appear on your driver record. Eighteen (18) months after the date of the violation, the points for that violation are removed from your point total. The convictions remain on your record for a longer period of time.
The NYS DMV states that the penalty for a seat belt or car seat violation is a fine of up $50. If a conviction includes a person under the age of 16, the driver receives a maximum fine of $100. The average fine amount likely differs from one NY jurisdiction to the next depending upon what the local courts have decided to have drivers pay, $50 or less, plus any administrative and court fees. Your husband of course can find out how much his seat belt ticket is by contacting the court listed on his citation.
The good news is that generally, this type of ticket or violation will not cause your insurance premiums to rise. However, there are some carriers that may remove discounts for safe driver, which is not technically raising your rates, but the bottom line is that your rates would go up.