Brightfield microscopy often suffers from limited depth of field, which prevents thick specimens from being imaged entirely in-focus. By optically sectioning the specimen, the in-focus regions can be acquired over multiple images. Extended depth of field methods aim at combining the information from these images into a single in-focus image of the texture on the specimen's surface. The topography provided by these methods is limited to a map of the selected in-focus image for every pixel and is inherently discretized, which limits its use for quantitative evaluation. In this paper, we propose a joint texture and topography estimation, based on an image formation model for a thick specimen incorporating the point spread function. The problem is stated as a least-squares fitting where the texture and the topography are updated alternately. The method also acts as a deconvolution operation when the in-focus image has some blur left, or when the true in-focus position falls in-between two slices. The feasibility of the method is demonstrated with simulated and experimental results.