Severe anxiety can cause a sense of breathlessness and vague disquiet in the chest. A heart attack is classically a constricting pressure in the chest, often with a feeling of impending doom and shortness of breath. However, a heart attack can present as stomach pain, neck or jaw discomfort, back pain, shoulder or left arm discomfort, just shortness of breath, and can sometimes be “silent” (without symptoms).
The sensation of a “pounding heart” would be very unusual for a heart attack. Heart rhythm disturbances (an irregular or rapid heart rate) can cause this symptom but it could also be from an adrenalin rush from being startled by a phone ringing in the night, or frightened by a suddenly dangerous situation, or intense and acute anxiety. If someone has a structurally normal heart, no coronary artery disease, and no fainting or near fainting, the symptom of a pounding heart is generally benign.
Getting the symptom evaluated to rule out a cardiac cause was a smart thing to do. If your husband does have a problem with stress and anxiety, dealing with it through counseling, meditation, yoga, and/or lifestyle changes should be considered.