Solutions to the differential equations governing the structure of a steady-state detonation in a spray are obtained both numerically and by means of analytical approximations for the case in which the droplets in the spray burn heterogeneously. It is shown that, for reasonable droplet burning rates, the detonation structure corresponds almost precisely to the spray analog of the von Neumann hypothesis of a shock wave followed by a deflagration zone. The size of the burning region is demonstrated to be large enough to cast doubt upon the stability of a spray detonation not supported to a significant extent by purely gaseous reactions.