Lots of good points made here.
The CF is concerned as much with the fact that you‘re taking the medication, but the ARE concerned about the underlying condition. If you have clinical depression, bipolar disorder, or other mental health problems, then your ability as a soldier is severely hindered. When put into extremely stressful situations, it can aggravate the condition, with or without meds, and you may not be able to cope.
You should speak to your doctor or psychiatrist (whoever prescribed the meds in the first place) and ask them about your condition. If your doctor thinks that your condition has improved enough to warrant taking you off meds, then they can do that, or change the prescription, or offer alternate therapy.
But, as was already stated, are you sure this is what you want to do with your life? Some of the situations in which you might find yourself could exacerbate your symptoms, and delay any kind of long term cure. You could end up far worse off than you ever were. Even if the military accepts you, are you prepared for that kind of risk?