Hi,
I'm not April, but we have used both homeopathy and naturopathy and I can explain that much.

Naturopathy looks at using diet changes, supplements, and sometimes bio identical substances to try and heal the body.
Homeopathy works on the basis of like cures likes. Minute amount of substances are used to bring the body into balance so it can heal. No extra supplements (although we use cell salts they are not a "supplement"). We basically eat a healthy diet but not anything in particular along with treatment.
We used naturopathy for more then 5yrs trying to heal our boy's immune system and what we ended up with was spending $15K and no healing. While it supported his body, he never healed. He didn't get worse until his ITP hit. At that point, the diet and supplements could no longer contain the damage. I think we staved things off, but didn't heal anything.
The homeopathy we have been using for a year. Our boy is exactly 1yr into treatment and I would dare say, nearly done. We are winding down. And he is healing very very well. The first immediate improvement was his ability to begin eating foods again that he'd been allergic to for years. It took just several months to accomplish that. We NEVER got to the point of even being able to try that with the naturopathy.
I think who you choose as your doctor will really make the difference in regards to your medical doctors. Drugs can slow down how homeopathy works but it's not insurmountable. Our homeopath had no contact with our doctor but did follow how blood work was coming back, etc. They really are two different paths so they don't work together per se. Just that the h-path will ask what test results say when they do come back. That's about it. And other h-paths may have varying degrees of involvement with an MD.
April can probably give you a much more technical explanation, but that is our experience with the two modes of treatment.
patti