This study presents a novel method that directly integrates SOFC oxy-fuel combustion and SOEC co-electrolysis to tackle the challenges of high-energy consumption of SOFC/SOEC integration and photovoltaic duck curve. To explore the viability of this method, a biomass-solar complementary scenario is pioneered and its performance is assessed from thermodynamic and economic standpoints. The results show that the studied scenario achieves CHP and exergy efficiencies of 50.67% and 43.68% with the corresponding total product cost rate (Ċtot) of 45.44 $/h and the levelized cost of products (cp) of 14.61 $/GJ under the design conditions. The system annually produces 17485 tons of freshwater and 1432 tons of oxygen. Exergy analysis identifies the afterburner (AB-II) and supercritical CO2 recompression power cycle (SCRPC) as the primary contributors to exergy destruction with 381.74 kW and 343.62 kW, which alone account for over half of the total irreversibility. Increasing the isentropic efficiency of gas turbine (ηGT) and SOFC operating pressure (Pop) improves the overall thermodynamic performance, but enhancing SOFC current density and gasification temperature has adverse effects. Across varying Pop and ηGT, there exist optimal Ċtot (44.83 $/h) and cp (14.47 $/GJ), which are obtained at ηGT of 80% and Pop of 600 kPa, as well as at ηGT of 87.14% and Pop of 800 kPa, respectively. This research can provide a reference for the development of cyclic energy storage technologies and the low-carbon transition in the energy fields.