The effects of alcohol and marijuana on the body and brain have been researched extensively, but being under the influence of both at the same time is a bit more of a mystery.
Alcohol and marijuana are often used together, though, and the results have been studied.
Marijuana contains THC (tetrahydrocannabinol), which is the key ingredient that affects cognitive functions and gives you that high.
Alcohol, on the other hand, dulls the central nervous system and will affect your brain in a different way. Drink enough of it and you'll lose some of your motor skills and rooms will start spinning.
A study was conducted in October 2001 by Scott Lukas to try and examine the effects of ethanol and THC. It found that after subjects had smoked weed and drank the equivalent of a few shots of alcohol, the THC levels in their blood was nearly double compared to those who smoked marijuana and had a placebo drink.
This means that if you were to combine smoking weed and drinking alcohol, you will most certainly get 'high' faster, as the THC can hitch a ride through your bloodstream.
So it's a safe bet to say that mixing the two can only increase chances of harm.