Oxycodone pretty much the same way. The hydrochloride/sulfate is very water soluble, the freebase is nearly insoluble. Codeine is a touch different, as it's freebase is somewhat solubile in water.
There is one thing I don't get, if one raises the pH of a solution of morphine hydrochloride, do the phenoxy groups dissociate and will it become a water soluble phenoxide?