Electrically and thermally conductive polymer composites (CPCs) have promising applications in flexible and wearable electronics, and it remains difficult for the trade-off between the electrical and thermal properties and the breathability. We propose a “MXene bridging graphite nanoplatelets (GNPs)” strategy to prepare conductive membranes with high conductivity and excellent breathability. Rigid GNPs are randomly distributed inside polyurethane nanofibers and expand the network. MXene nanosheets are decorated onto the nanofibers and bridge GNPs to reduce the thermal and electrical contact resistance. The synergy of MXene and GNPs improves electrical and thermal conductivity without sacrificing their breathability. The electrical and thermal conductivity of the composites can reach 64.4 S/m and 4.9 W (m K)−1, respectively. In addition, the nanofiber composites with strong interfacial interactions and thus superior durability show outstanding photothermal conversion and heat dissipation capability. This study can provide inspiration for designing multi-functional, breathable CPCs with potential applications in wearable electronics.