Recent advances in multiplexed fluorescence imaging have provided new opportunities for deciphering the complex spatial relationships among various cell types across diverse tissues. We introduce CytoSpatio, open-source software that constructs generative, multirange, and multitype point process models that capture interactions among multiple cell types at various distances simultaneously. On analyzing five cell types across five tissues, our software showed consistent spatial relationships within the same tissue type, with certain cell types like proliferating T cells consistently clustering across tissue types. It also revealed that the attraction-repulsion relationships between cell types like B cells and CD4-positive T cells vary with tissue type. Models for a published dataset demonstrated consistency with prior findings. CytoSpatio can also generate synthetic tissue patterns from learned models, a capability not provided by previous descriptive, motif-based approaches. This potentially allows spatially realistic simulations of how cell relationships affect tissue biochemistry.