Involved in the assembly of several proteins in the inner and outer layer of the spore coat. Stabilizes CotC and CotU in the mother cell compartment of sporulating cells and promotes the assembly of both early and late forms of CotC-related polypeptides on the spore surface. Assembly of CotH requires CotE and GerE. Expression is negatively regulated by the transcriptional regulator GerE. Belongs to the CotH family.