You are correct in your concern for interactions between alcohol and doxepin. The specific concern is just as you have mentioned: depression
of the central nervous system (brain and spinal cord).
CNS depression can have many symptoms, but the most common are an increased sense of sleepiness or drowsiness. Effects seen at higher doses can be difficulty walking or slurred speech. Dangerous side effects at higher doses are respiratory depression, which can lead to stopping breathing (typically after falling asleep), coma or death. The likelihood of these medications producing a dangerous interaction increase with the dose, so the more you drink the more likely you are to have these effects, as well as with other medications or substances which also produce CNS depression. The doses of doxepin typically used for insomnia
are lower than the doses used for other reasons, but in general, patients taking doxepin are not advised to drink any alcohol. You should definitely consult with your doctor
prior to taking any other medication, and although it is not advisable to drink any alcohol at all, should you choose to do so, you should do so with great caution and avoid any compromising situations (i.e. driving, operating machinery, swimming).
Of note, among the other potential side effects of doxepin is an FDA "black box" warning about suicidal ideation. While rare, there is a documented association of doxepin and suicidal thoughts and behaviors. Should you find yourself thinking of causing harm to yourself or others at any point, you should contact your doctor or an emergency medical service (either by phone or by going to the emergency room) immediately.