Sedation of the Central Nervous System is the primary problem with combining depressants. The main issue that usually arises from this "slowing" of the CNS is respiratory depression, which kills through hypoxia. In conservative doses, you shouldn't have anything to worry about. Combinations of CNS depressants are often prescribed and in the hands of a trained anesthesiologist, various combinations of Opioids, Barbiturates, Benzodiazepines and Volatile Gases are combined to completely numb the body's senses.
So yes, they can be used together, if done so with a certain degree of responsibility. When used compulsively or addictively, it becomes much easier to make mistakes and overdose yourself. One scenario might include someone with limited tolerance taking 5mg of Oxycodone with their nightly dose of say, 1mg of Alprazolam or equivalent. Another scenario might include a Heroin addict, using anywhere from 5 - 20 points/bags per day depending upon ability, haphazardly consuming Xanax bars throughout the day to help them get more mileage out of their limited Opioid supply. The second scenario, as you can probably ascertain, is going to be significantly riskier than the first.
I'm just giving you these situation to illustrate the difference between "responsible" use of these combinations as well as the more reckless. As with everything in life, moderation is the key.
As far as Alcohol is concerned; it's a poison. It's inherently toxic to the body and is destructive to just about every organ or system necessary for life. So, if you're looking to improve your quality of life from the ground up, Alcohol should be excluded. Aside from the well known physical drawbacks of Alcohol consumption, there are a myriad of psychological issues that accompany its use. Depression, anxiogenesis, confusion etc. are all possible sypmtoms of Alcohol abuse.
So, when someone decides that they're going to attempt to improve their overall mood with an SSRI or similar antidepressant, it must be taken into account that Alcohol, which we know to affect all of the body's systems negatively, will almost certainly interfere with the potential benefits of SSRI therapy. To experience and actually notice the subtle effects of an SSRI, one would probably want to start from a point of relative homeostasis i.e. not dependent on drugs, not introducing new drugs into the body etc.
If your body is constantly in a state of flux from Alcohol use, it's unlikely that you'll be receiving the full benefit from your antidepressant. I'm not saying that antidepressant therapy is going to be completely useless to Alcohol users, but iuf you're really looking to make positive changes for yourself, from a logical standpoint, Alcohol should be excluded. There are other recreational experiences which are much safer/healthier and more rewarding anyway. Also, I've already alluded to this, but chronic Alcohol use invariably leads to depression and anxiety.
Just a few things to think about. I'm in no way preaching to you OP, just giving you my opinion.
