We investigate the rheology of biphasic fluid systems comprising an elastoviscoplastic (EVP) matrix fluid containing initially spherical, monodisperse, viscous droplets through interface-resolved numerical simulations. The interface is captured using the level-set method, and the EVP phase is modeled with the Saramito constitutive equation. We explore the effects of the volume fraction, capillary, Weissenberg, and Bingham numbers, considering both dilute and semidilute regimes (dispersed phase volume fractions from 0.16% to 20%) at two density and viscosity ratios. The constitutive curve shows a negative curvature, consistent with previous studies on emulsion rheology with coalescing drops. Increasing the capillary and Bingham numbers show qualitatively similar trends: increasing drop deformation with both results in a decrease of the system's relative viscosity. This is further supported by stress budget analysis, which shows that yield stress increases the effective viscosity of the matrix fluid, thereby increasing the effective capillary number and reducing the effective viscosity ratios. The bulk rheology shows a complex relationship with the Weissenberg number (Wi). In dilute systems, droplet deformation increases with Wi, while bubbles exhibit a nonmonotonic trend. Relative viscosity rises with Wi for emulsions up to Wi = 1.75 due to localized EVP stresses, then slightly decreases. For bubbly suspensions, the viscosity shows little variation at low Wi but decreases at larger values. At semidilute concentrations, similar trends emerge with EVP stresses dictating the system's bulk rheology. At high Wi, increased EVP stresses, reduced coalescence, larger interfacial stress, and near-wall droplet migration collectively increase emulsion relative viscosity.