As a native speaker and writer of American English, to "describe a process" is a valid usage, but the result is more of a narrative than the description you'd get from "describe an object." Obviously, you can't give the color, shape, texture, aroma, etc. of the process of becoming a Christian, or your relationship with your mother -- though the latter is closer to a "descriptive" essay than the former, because you can tell how a relationship makes you feel, what you gain and give, and so forth.
If you have the ability to ask the instructor for clarification, I'd start by doing that. If you assignment is primarily about your distinguishing between descriptive and narrative essays, there are likely to be clues in your lecture notes or text on how your instructor wants you to accomplish this. To me, without additional information this assignment appears likely to be about the "gray area" (note American spelling) between description and narrative.
Unfortunately, usages vary tremendously between different versions of English -- Americans and Canadians often disagree on subtle points, never mind Londoners, Australians, Indians from different pradesh, those who learned English as a native language in Hong Kong before the return to China or those who learned it there after. English is one of the most difficult languages to learn fluently as a second language because it is so internally inconsistent. If you're not in an American college, my answer may not be much help.