Since his position genuinely requires travel as part of his job duties, and he informed them during the interview that he would not relocate, you could consider the days he worked outside of New York as "employer necessity" rather than personal convenience. In this case, you would only need to report the income he earned while he was physically present in New York.
In the event that New York requests documentation proving that this would not be considered New York source income, you should maintain detailed records of work locations, document that travel is a requirement of the position, and keep any documentation that shows the employer acknowledges your husband works primarily outside of New York.
