One of the most fundamental processes in the bacterial life cycle is division. This process is mediated by the divisome, a multi-protein complex whose core subunits are conserved across bacterial phyla. Though many protein-protein interactions between divisomal subunits are known, there is very little information on how these interactions are mediated. Additionally, most divisome proteins have essential transmembrane domains that resist biochemical characterization. By taking advantage of computational protein structure prediction and the vast evolutionary sequence record for divisomal proteins, it may be possible to determine how divisome proteins associate and carry out cell division. For example, the intermediate divisomal proteins FtsB and FtsL exhibit a large number of strongly coevolving positions that span their transmembrane and periplasmic domains. With this information, the FtsB-FtsL subcomplex was modeled as a four-helix bundle that is consistent with the coevolutionary data as well as mutagenesis experiments, single-molecule studies of FtsB-FtsL stoichiometry, and molecular dynamics simulations. The coevolving positions in FtsL were consistent with a continuous helix spanning the transmembrane and coiled coil domains, but in FtsB the transmembrane interface was shifted relative to the coiled-coil interface. This shift is mediated by a conserved glycine-rich juxtamembrane region of FtsB which may allow conformational flexibility. Other proteins within the bacterial divisome also have strong coevolutionary signals, which will be useful for modeling their interactions and identifying important interfaces where bacterial cell division might be disrupted.