•Hybrid base isolation of a historical masonry church.•Unbonded fiber reinforced elastomeric isolators and shape memory alloy wires.•Increase of the energy dissipation capacity.•Detailed 3D FE models to characterize the cyclic behavior of UFREIs.•Abaqus user element (UEL) to represent the 3D behavior of the isolators for global analyses. One of the most promising devices for seismic base isolation of structures is the Unbonded Fiber Reinforced Elastomeric Isolator (UFREI) due to its low manufacturing cost and horizontal stiffness. This paper investigates the possibility of combining UFREIs and shape memory alloy (SMA) wires to increase the energy dissipation capacity of the isolation system for the seismic protection of a historical masonry church. Detailed 3D finite element (FE) analyses are performed to characterize the response of UFREIs under cyclic displacements. The behavior of SMA is simulated through a thermomechanical constitutive model implemented in a user-defined material (UMAT) subroutine available in the software package Abaqus. To reduce the computational effort in non-linear dynamic analyses of large isolated structures, an Abaqus user element (UEL) is developed to represent the 3D behavior of the isolation system proposed in this study. Non-linear dynamic time history analyses are then carried out to evaluate the seismic response of a historical masonry church in different configurations (fixed-base model and model equipped with different base isolation systems) for moderate and severe seismic intensity levels. Numerical results show that the damage observed in the masonry church can be considerably reduced through the insertion of UFREIs. The utilization of SMA wires with a specific pre-strain significantly increases the energy dissipation capacity of the base isolation system and decreases the horizontal displacements of the masonry church.