Spatially resolved transcriptomics (SRT) technologies measure messenger RNA (mRNA) expression at thousands of locations in a tissue slice. However, nearly all SRT technologies measure expression in two-dimensional (2D) slices extracted from a 3D tissue, thus losing information that is shared across multiple slices from the same tissue. Integrating SRT data across multiple slices can help recover this information and improve downstream expression analyses, but multislice alignment and integration remains a challenging task. Existing methods for integrating SRT data either do not use spatial information or assume that the morphology of the tissue is largely preserved across slices, an assumption that is often violated because of biological or technical reasons. We introduce PASTE2, a method for alignment and 3D reconstruction of multislice SRT data sets, allowing only partial overlap between aligned slices and/or slice-specific cell types. PASTE2 formulates a novel fused Gromov-Wasserstein optimal transport problem, which we solve using a conditional gradient algorithm. PASTE2 includes a model selection procedure to estimate the fraction of overlap between slices, and optionally uses information from histological images that accompany some SRT experiments. We show on both simulated and real data that PASTE2 obtains more accurate alignments than existing methods. We further use PASTE2 to reconstruct a 3D map of gene expression in a embryo from a 16 slice Stereo-seq data set. PASTE2 produces accurate alignments of multislice data sets from multiple SRT technologies, enabling detailed studies of spatial gene expression across a wide range of biological applications.