An internally-manifolded solid oxide fuel cell (SOFC) stack is described, including an anode interconnect structure 12 integrated with a cathode interconnect structure 14. The anode interconnect structure 12 includes a fuel flow field 24; and the cathode interconnect structure 14 includes an air flow field 26. The two structures are configured to allow for parallel flow of air and fuel across a plane of the interconnect 10, while the manifold openings for the fuel 16,18 are arranged in a cross-flow orientation with respect to the manifold openings for the oxidant (20, 22) across a plane of the interconnect structure 10. Related processes are also described, along with a power generation system that includes an SOFC incorporating this type of interconnect 10, attached directly or indirectly to at least one power block, such as a combustion engine.