Uses of hiragana: 1. All types of native words (you were correct in using the term native) other than nouns, verbs, and adjectives. 2. Nouns, verbs, and adjectives whose kanji doesn't exist or is obsolete.(ex. isu-chair suru-to do/make ureshii-happy) 3. Inflectional endings of all words written in kanji (like the ru in miru-to see or the i in aoi-green/blue)
Uses of kanji: The roots (tabe in taberu-to eat ao in aoi-green/blue) of nouns, adjectives, and verbs which are native to the Japanese language.
Sorry for not typing the characters, it takes me a long time to do it on the computer, but I hope this was sufficient information.