Here is what really happens:
Mixing bleach and ammonia is extremely dangerous, since toxic vapors will be produced. The primary toxic chemical formed by the reaction is chloramine vapor, with a potential for hydrazine formation. Here's a look at the chemical reactions involved in mixing bleach and ammonia, as well as some first aid advice if you accidentally become exposed to a bleach and ammonia mixture.
Chemicals Involved
Note that each and every one of these chemicals is toxic, except for the water and salt.
NH3 = ammonia
HCl = hydrochloric acid
NaOCl = sodium hypochlorite (bleach)
Cl = chlorine
Cl2 = chlorine gas
NH2Cl = chloramine
N2H4 = hydrazine
NaCl = sodium chloride or salt
H2O = water
Likely Chemical Reactions from Mixing Bleach and Ammonia
The bleach decomposes to form hydrochloric acid, which reacts with ammonia to form toxic chloramine fumes:
First the hydrochloric acid is formed:
NaOCl -> NaOH + HOCl
HOCl -> HCl + O
And then the ammonia and chlorine gas react to form chloramine, which is released as a vapor:
NaOCl + 2HCl -> Cl2 + NaCl + H2O
2NH3 + Cl2 -> 2NH2Cl
If ammonia is present in excess (which it may or may not be, depending on your mixture), toxic and potentially explosive liquid hydrazine may be formed. While impure hydrazine tends not to explode, it's still toxic, plus it can boil and spray hot toxic liquid.
2NH3 + NaOCl -> N2H4 + NaCl + H2O
Taken from:
http://chemistry.about.com/od/toxicchemicals/a/Mixing-Bleach-And-Ammonia.htm