Geometrically exact formulations provide a rigorous basis for nonlinear structural analysis in situations where bodies undergo large translations and rotations while strains remain small. For both thin-walled components and slender members, geometrically exact shell and beam theories can be consistently formulated on the Lie group SE(3), enabling a unified description of large rigid-body motions and small strain measures. In shell theories, the motion of the shell director field is described with full kinematic consistency, naturally capturing membrane–bending coupling. Similarly, geometrically exact beam theories on SE(3), often implemented via co-rotational descriptions, provide an efficient and robust treatment of large rotations with small strain measures. Lattice boom structures of mobile cranes, which combine shell-like panels with beam-like pipes, represent a typical application that motivates a coupled analysis framework integrating both formulations within a single computational model. This paper presents a combined beam–shell formulation that unifies a geometrically exact shell model and a geometrically exact beam model, both consistently posed on the Lie group SE(3) and sharing a common rotation parametrization and update scheme. A kinematically compatible interface is introduced to relate beam centerline variables to shell midsurface variables, enabling the transfer of displacements, rotations, and stress resultants without inducing locking effects or artificial constraint stiffness. The coupling between the connected structural components is enforced by shared interface nodes, so compatibility is satisfied directly through the finite element connectivity. The resulting discretization preserves objectivity, accommodates large rigid-body motions, and retains the benefits of small-strain constitutive modeling. Representative numerical studies of shell-reinforced beam assemblies, inspired by lattice boom structures of mobile cranes, illustrate the ability of the proposed formulation to capture geometric nonlinearity, local shell response, and beam–shell interaction effects. The results demonstrate improved robustness and accuracy compared to uncoupled analyses and provide a foundation for efficient simulation of complex industrial beam–shell structures encountered in demanding engineering applications.