A novel class of boundary conditions is introduced as a generalization of the previously defined class of soft-and-hard/DB (SHDB) boundary conditions. It is shown that the conditions for the generalized SHDB (GSHDB) boundary arise most naturally in a simple and straightforward manner by applying 4-D differential-form and dyadic formalism. At a given boundary surface, the GSHDB conditions are governed by two one-forms. In terms of Gibbsian 3-D vector and dyadic algebra, the GSHDB conditions are defined in terms of two vectors tangential to the boundary surface and two scalars. Considering plane-wave reflection from the GSHDB boundary, for two eigenpolarizations, the GSHDB boundary can be replaced by the perfect electric conductor or perfect magnetic conductor boundary. Special attention is paid to the problem of plane waves matched to the GSHDB boundary, defined by a 2-D dispersion equation for the wave vector, making the reflection dyadic indeterminate. Examples of dispersion curves for various chosen parameters of the GSHDB boundary are given. Conditions for a possible medium, whose interface acts as a GSHDB boundary, are discussed.