A novel dual tank photovoltaic/thermal (PV/T) indirect parallel solar-assisted heat pump system was investigated in this paper, which filled a gap in the literature. Furthermore, a long-term performance study analysis was performed under Tunisian climate to offset domestic electric and hot water loads. Optimal operations of such a system are achieved based on a simplified mathematical model. Results showed that the average thermal and electric energy efficiency is about 39.65% and 11.38%, respectively. Results revealed that the increase in solar radiation results in an improvement of the system's thermal-based coefficient of performance efficiency coefficient reaching 4.49 at 893 W/m2. PV/T average electrical energy output is found to 0.68 kW h/m2/day with an annual average of 177.42 kW h/m2, which leads to an annual electricity surplus of about 5.83%. A reversible heat pump operation seemed more advantageous especially in the summer months, reducing yearly electric demand by about 84.57%. An economic analysis is undertaken and a payback period of about 12.7 years is found. The current study provided a framework for assessing such a system's behavior and providing useful flexibility to achieve the best possible system performance.