Is  NCl3 + 3H2O ---> 3HClO + NH3 considered an acid/base reaction? If not, what type of reaction would this be classified as?

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Typically, an acid + base reaction would involve an acid being mixed with a base as reactants, on the left side of the yields sign.  The way you have this equation constructed, the acid and the base are being produced, because they are on the right side of the yields sign, where the products go.  So I don't think it would be fair to call it an acid + base reaction.  It could be a synthesis reaction, which is when you add two reactants together and they produce one or more products.  It could also be an equilibrium reaction, which is what you get, when the reactants combine to form the products, then the products recombine to become the reactants.  Sort of like a "back-and-forth" ping-pong game between the two sets of compounds.  An equilibrium reaction would have a double arrow where the yields sign is, like this:  <--->.  Usually, when you combine a strong acid with a strong base, the product is not in equilibrium, and it forms a salt plus water.

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