Dishwater is hooked up with the garbage disposal. For past couple of days I have noticed that when dishwasher runs there is water coming out from the air vent in the sink which is coming up from garbage disposal.

Please help

I think you have confused a few plumbing terms here. Your dishwasher drain line may be hooked to the garbage disposal but that is a drain line only. If there is a back up it will fill up the sink via the drain in the sink. Some dishwashers are installed with a dishwasher air gap on the sink counter and that is the water line that fills the dishwasher. It can back up if there is an obstruction in the second half of the line. Dishwashers do not have an air vent that is shared with the sink, actually kitchen sinks don't have air vents. Can you describe your issue differently or explain further?
Thanks

Dishwater is hooked up with the garbage disposal. For past couple of days I have noticed that when dishwasher runs there is water coming out from the air vent in the sink which is coming up from garbage disposal.

Please help
You have a clog in the horizontal drai line in the wall. Let me explain. Your disposal table acts like a centrifugal pump when it's running. The water in your disposal hits the clog under pressure and backs up into the dishwater air gap where it comes out on the counter top. The solution would be to remove the "J" bend from the trap and sen a snake up inti the wall. you'll hit a elbo about 8 inches in but work around that and you'll only have 6 more feet of cable to run out. Good lucj, Tom