They are part of RAAChD, and then they are often posted to a unit (as the unit padre), and so become part of that unit as well. So I can assume that PADRE serves in a Health Support Battalion or a CSSB unit.
No, qualified and uniformed in both :CG: :army: but will only belong to Navy in a year's time. :dive: Doing both because of the chronic shortage of padres. I've heard the US Defences are desperate for more chaplains but this may not be accurate.