To explore the intersection of previous studies of inert mixed-mode flows and single-mode diffusion flames, this analysis describes a laminar, forced and free, mixed-mode diffusion flame adjacent to a vertically burning fuel slab. Shvab-Zeldovich variables, boundary-layer and local similarity approximations are used. Five flaming and chemical parameters are found necessary to describe this combusting system. The solution obtained herein includes profiles of velocity, Shvab-Zeldovich variables and thereby enthalpy and species, as well as surface fluxes, flame sheet locations and excess pyrolyzate. For comparison, the finite-difference method is also employed. The local similarity solution for surface gradients lies within 20 percent of the finite-difference results. Good agreement with the aforementioned simpler limiting cases is also obtained. The results indicate that the flow characteristics of a mixed-mode flame are more complicated than a simple superposition of the two limiting flame cases.