Many people feel that what they are going through is a religious experience and not a mental illness. A good way to counter this type of thought, is to look at the facts with them.
If you have a mental illness, what you will portray is symptoms, and if you are having a crisis of faith, you will portray certain things as well. Best to look at the facts first. A crisis of faith isn't usually the end of the line for you. Most religions have a way to reconcile yourself. A mental illness will not go away so easily.
If you find that your symptoms are not going away after you have done the acts needed to reconcile yourself in whatever way your faith asks you to do, you may find that taking a look at the symptoms of mental illness to be the next step.
Sometimes someone you know might feel that even though the evidence shows them they are not going through a crisis of faith, they still may believe they are. By going through the symptoms of the mental health disorder that a doctor or therapist might feel your loved one has, you might find some answers, and easy ways to explain to them what they are really going through.
Don't expect it to all come make sense at once, but it will come clear with time and patience. When you weigh all the evidence at once, it can be easier for someone to accept that what they are going through is treatable, instead of something of doom.