Can you have both influenza a and influenza b at the same time?

Yes. : Although rare, it does sometimes happen. Last week i had a little girl who presented with influenza symptoms, and tested positive for influenza a in my office. I am part of a dept of health survey site, and sent an additional specimen to the state lab, which identified both influenza a and b in this unfortunate girl. She recovered with tamiflu (oseltamivir).