Spatial microsimulation models typically match census of population data with survey data in order to simulate synthetic populations of individuals and households within small-scale geographic areas. For most spatial microsimulation applications this level of spatial precision is satisfactory. For others, more precise information on the location of simulated units may be required. To this end this paper develops a continuous space representation of a simulated population. It presents a statistical matching approach for assigning simulated households from a spatial microsimulation model to unique spatially-referenced residential locations. The allocation is based on a random assignment after splitting the simulated households into two groups: those predicted to reside in apartments and those predicted to reside in houses. The resulting 'geohouseholds' have a range of potential applications in economic and spatial analysis.