Mixed cocrystals derived from electron-rich donor (D) and electron-deficient acceptor (A) molecules showcase electronic, optical, and magnetic properties of interest for a wide range of applications. We explore the structural and electronic properties of a cocrystal synthesized from dithieno[3,2-a:2',3'-c]phenazine (DTPhz) and 7,7,8,8-tetracyanoquinodimethane (TCNQ), which has a mixed-stack packing arrangement of the (π-electronic) face-to-face stacks in a 2:1 D:A stoichiometry. Density functional theory investigations reveal that the primary electronic characteristics of the cocrystal are not determined by electronic interactions along the face-to-face stacks, but rather they are characterized by stronger electronic interactions orthogonal to these stacks that follow the edge-to-edge donor-donor or acceptor-acceptor contacts. These distinctive electronic characteristics portend semiconducting properties that are unusual for semiconducting mixed cocrystals and suggest further potential to design organic semiconductors with orthogonal transport characteristics for different charge carriers.