No, most likely not.  This is because the main purpose for an instruction permit is so that the driver may receive proper training prior to actually getting his/her license to drive.   Teenagers with a permit are allowed to drive while under the supervision of the guardian who signed the permit application, or with an approved third-party organization (Driver's Education Program).   However, because the permit is to allow drivers to get hands-on training under constant supervision, driving your parents while they are intoxicated would not meet the criteria of constant supervision. Therefore, you'd want to make sure that your parents were not under the influence while you were learning how to drive from them.

The law does not give an easy answer to kids who are trying to do the right thing in light of their parents' drinking.  The best thing is to try to have someone sober drive in that situation or arrange alternate transportation (such as a taxi or bus).  If there is no other choice, you could call the police station and explain the situation to them - they may be able to help you with a decision. 

You can visit the Department of Motor Vehicles on-line for more information about driving permits.