If I don't have hepatitis a, b, or c could my partner have it and me not?

Yes. Hepatitis A (HAV) is contagious via contaminated food, water, Hepatitis B (HBV) and C (HCV) are transmitted through exchange of body fluids; sex, sharing of needles, tattoos, blood transfusions, newborn from an infected mother. HAV is never a chronic illness. HCV and HBV can lead to chronic liver disease. HCV may cause liver failure, liver cancer. Can have infection with no symptoms. Get tested.
Yes. It is very possible for your partner to have any type of viral hepatitis and for you not to catch it. Of these, only hepatitis B is actually usually transmitted by sex. If you have questions, either or both of you can be tested for abnormal liver tests and for hepatitis. Good luck.