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@cyberia So, long story short, the ammonium hydroxide/hydrogen peroxide thing? There's no reaction there*. As far as I can tell, they don't actually react. Instead, it's two separate bleaching agents being used simultaneously. So, there isn't some stoichiometrically optimal ratio to mix them. As for getting rid of pigmentation, both react with pigments in a way that destroys their ability to absorb light, but I'm honestly not sure exactly what's going on.
@cyberia *Well, kinda. As far as I can tell, the ammonium hydroxide and hydrogen peroxide don't react with each other. But there would likely be an equilibrium reaction between ammonium hydroxide ((NH4)(OH)) and ammon*ia* + water (NH3 + H2O). I'm not sure how important this is towards the bleaching effect, but it's a caveat to "no reaction" I thought I'd mention.