You are quite correct in saying that science cannot delve into the supernatural or the spiritual. It can however at times explain the seemingly supernatural or spiritual as quite natural as in my recent post about Out of Body Experiences
Many such phenomena that we once believed to be spiritual/supernatural have turned out to have very quantifiable, measurable explanations. This does not mean that all such experiences will have such an explanation, but it should be enough to loosen any believe that a lack of explanations means it is of supernatural origin.
One of the most frustrating aspects in dealing with the highly religious is the "God did it" syndrome which essentially ends all discussion or research into the matter.