We present a novel method for detecting and quantifying 3D structure in stacks of microscopic images captured at incremental focal lengths. We express the image data as stochastically generated by an underlying model for biological specimen and the effects of the imaging system. The method simultaneously fits a model for proposed structure and the imaging system's parameters, which include a model of the point spread function. We demonstrate our approach by detecting spores in image stacks of Alternaria, a microscopic genus of fungus. The spores are modeled as opaque ellipsoids and fit to the data using statistical inference. Since the number of spores in the data is not known, model selection is incorporated into the fitting process. Thus, we develop a reversible jump Markov chain Monte Carlo sampler to explore the parameter space. Our results show that simultaneous statistical inference of specimen and imaging models is useful for quantifying biological structures in 3D microscopic images. In addition, we show that inferring a model of the imaging system improves the overall fit of the specimen model to the data.