This work investigates the techno-economic performance of a hybrid photovoltaic-thermal (PVT) solar-assisted heat-pump system for covering the electrical and hot-water demands of a three-bedroom terraced house in Belfast, United Kingdom with four occupants. This system combines a water-to-water heat pump with PVT panels to deliver both electricity and hot water for domestic consumption. The PVT array provides a source of low-temperature heat for the water-to-water heat pump, while cooling the PVT array and thus preventing the electrical efficiency degradation that occurs at higher operating temperatures. Analyses have been performed for PVT arrays of different size, including 12-panel, 20-panel and 24-panel systems. Results show that, thanks to its lower initial investment cost, the most economically viable system configuration for the household considered in this work is based on a 12-panel PVT array covering a total area of 16.3 m2. This system has the potential to produce 2.4 MWh of (gross) electricity and 2.0 MWh of hot water per year, which is equivalent to just over 30% of the electrical and 80% of the hot-water demands of the household under consideration, with the PVT array acting to reduce the electricity consumption of the heat pump in the heating system by a little over 60%. The system has lower recurring yearly costs relative to current household energy systems that use electricity from the grid and natural gas, despite having higher investment costs. It is also found that the system can reduce the investigated household's annual CO2 emissions by 910 kg per year (about 18 tonnes over a lifetime of 20 years) and that, with an electricity generation incentive rate of 5 p/kWh and a heat generation incentive rate of 21 p/kWh, the aforementioned system has a discounted payback period of 14 years.