Jessica is a detective. A good one, in-fact, so it is entirely within the realm of possibility that Jessica could figure out that her teen son would be New York's newest vigilante. Matthew could also find out since he is essentially a Living Lie Detector, and Matt would of course know every tell his son has if he ever lies to him. That being said, they will probably look the other way considering he would be a teenager and would naturally want to keep secrets from them.
Odds are Tony will knock on Jessica's door and try and sell her the idea of the Stark internship. She'll play along and let him into her apartment, only to pin him to the wall and ask what's really going on.