Interlayer excitons formed in two-dimensional transition metal dichalcogenide (TMD) heterostructures can be easily tuned due to the large spatial separation. In this work, we discuss the electronic and excitonic optical properties of trilayer heterostructures MoS2/MoSSe/WSe2 and MoS2/MoSSe/MoSe2 using state-of-the-art GW+BSE calculations. In both trilayer geometries, we discover a variety of exciton states, including interlayer excitons, every-other-layer excitons, and their hybridized states, h-IX. Importantly, the h-IXs are optically bright through hybridizing with the intralayer excitons, and the radiative lifetimes of h-IXs range from subnanoseconds to tens of microseconds at 77 K, depending on their compositions. We also reveal that the diversity of the low-lying IXs in MoS2/MoSSe/MoSe2 is higher than that of MoS2/MoSSe/WSe2, because more energy levels participate in transitions in MoS2/MoSSe/MoSe2. Our findings demonstrate that the appropriate energy alignment via manipulating the Janus layer is crucial for realizing rich excitonic states in trilayer TMD heterostructures.