Each discipline has its own established methodologies. Perhaps you should seek one that is accepted in both disciplines or used a mixed methods approach by blending a methodology from each.
In my experience it depends on the disciplines being intersected and the question being addressed. It is important that the work is relatable to all relevant fields and therefore should draw methodology from each. There will be overlap in methodologies with some confusing differences in terminology, but also some real differences in approach. Where differences in approach exist it is useful to compare each approach to understand which is more useful.
I found statistics the worst aspect to handle - different disciplines often pick niche methods that are shared without rigorous challenge because they 'worked' (i.e. gave the answer they wanted) for someone in that field and it became accepted as THE WAY. It is important that combined methodologies are traced back to first principle rather than simply hoping one field or the other has got it right.