The seismic vulnerability of unreinforced masonry (URM) structures and their extensive presence worldwide has driven significant efforts in the assessment and retrofit of existing buildings and in the design and detailing of new constructions. The seismic performance of existing URM buildings is often compromised by local overturning mechanisms, as these constructions were predominantly conceived without consideration of horizontal forces. However, even if local failure is prevented through structural interventions or adequate construction details, the capacity of the structure might still be inadequate to withstand the in-plane demand imposed to the resisting elements. For this reason, common strengthening solutions often involve materials with significant tensile strength, such as fabric-reinforced cementitious matrices, composite-reinforced mortars, near-surface-mounted bars, steel or timber exoskeletons, applied to one or both sides of the masonry walls. This paper presents a novel three-dimensional equivalent-frame macroelement that captures the biaxial response of unstrengthened and strengthened masonry walls under lateral loads. The proposed model extends a pre-existing two-dimensional formulation, resorting to a computationally efficient axial-flexural integration to simulate the nonlinear static and dynamic behavior of masonry panels with a limited number of degrees of freedom. Furthermore, taking advantage of the versatility of the proposed three-dimensional formulation, additional lumped and distributed reinforcement is incorporated into the macroelement, enabling the explicit modeling of several reinforcing and strengthening layouts. The capability of the resulting macroelement formulation in reproducing lateral strength and stiffness, hysteretic cycles, and displacement capacity of masonry panels, is finally validated against experimental outcomes.