Hi Katy,
You've asked a number of questions here, so let me try to answer them one by one. 
First off, congrats to your husband for quitting smoking. Unfortunately, as he has found out, smoking can take a toll on our airways. Asthma is one result. Emphysema and chronic bronchitis are also common. Hopefully, he has quit early enough that his airways can heal and not get any worse.
Chest x-rays are not useful in diagnosing or evaluating asthma. So the fact that your husband's lungs were clear on x-ray is great, but has no direct bearing on his asthma. You'll find lots of information on asthma throughout this site, but basically it is an inflammatory disease of the airways, in particular the bronchial tubes. When your husband comes into contact with certain things called triggers, it kicks off a reaction in his body that results in a narrowing and swelling of his airways. And that causes symptoms like coughing, tightness in the chest, shortness of breath and wheezing.
Those triggers can vary from person to person, but commonly include things such as:
- Allergens such as pollen, dust, and animal dander
- Secondhand smoke or wood smoke
- Strong fumes or chemical odors
- Sawdust or talcum dust
- Cold, dry air
- Air pollution/car exhaust
The preferred treatment for most asthma is an inhaled steroid, so I suspect that's what your husband has had prescribed. It is extremely important that he take that every day exactly as prescribed, even when he feels great and his x-rays are clear. Taking the medicine will help keep his asthma under control and prevent serious asthma attacks or even more minor symptoms.
Anxiety and stress can be triggers for asthma, and when severe can definitely be a factor in how well controlled asthma is. But anxiety and stress alone do NOT cause asthma. This is a very real disease of the airways, caused by a variety of genetic and environmental factors. It is not an emotional illness or "all in the head," despite what may have been believed in the past.
Take care,
Kathi