3D-printable conductive polymers are gaining remarkable attention for diverse applications, including wearables, pressure sensors, interference shielding, flexible electronics, and damage identification. However, the relationship between the anisotropy of their mechanical and electrical properties remains rather unexplored. This study focuses on characterizing Polylactic Acid/Carbon Black nanocomposites manufactured through fused filament fabrication. It aims to investigate the effect of the orientation of 3D printing layers on the mechanical properties, failure mechanisms, and self-sensing capabilities of the 3D printed material. To this end, we use a coupled health monitoring system in which electrical resistance measurements are applied to diagnose the damage state of 3D-printed samples during tensile testing. The results provide novel insights into the strong dependence of the material behavior on 3D printing pattern orientation, suggesting avenues for optimizing mechanical and electrical anisotropy through a multi-objective approach. Additionally, they offer guidelines for designing self-sensing components for structural health monitoring applications and strain gauge sensors with superior performance.