First make an appointment with his pediatrician to rule out a medical reason for his crying. If there are no medical problems, the pediatrician may treat it as though your child has formed a bad habit that needs to be broken in an acceptable way.
Breaking bad habits is not easy, and it will take a commitment. If the doctor says he needs to cry it out, there will be some rough nights ahead of you and your husband. Keep the goal in mind and stick to it. You and your husband will lie awake listening to the screaming, but do not break your agreement. "
If the doctor recommends a window of time for him to cry, respect that. He may even suggest that if you do respond, you do not pick him up or put him into your bed. Instead, speak in a soothing voice, lay him back down, give him his security blanket or stuffed animal, rub his back and sing him a lullaby. This is a phase that will pass if you make a commitment to change it.