The utilization of lightweight construction is one of the keys to increase the fuel efficiency and reduce the environmental effect of automobiles. Natural fiber composites are replacing expensive synthetic fibers increasingly commonly in the automotive sector. To further lower the weight and price of the vehicle without losing rigidity and strength, basalt (B) fiber could be incorporated into jute (J) fiber composites. For the generation of hybrid composite laminates, woven textiles made of J-fiber and B-fiber were combined with an epoxy matrix. The primary mechanical features of the J-B/epoxy composite laminates, including tensile, bending, shear, and bearing characteristics, were investigated. Hand lay-up approach was used to prepare the hybrid composite laminates. The impact of the number of J-plies relative to the number of B-plies on the mechanical properties was explored. The findings proved that the basalt/epoxy composite has the maximum ultimate tensile strength, young’s modulus, toughness modulus, bending strength, bending modulus, in-plane shear strength, and bearing strength. Whereas the J/epoxy composite showed the maximum failure strain and bending strain. Hybridizing J-fiber with B-fiber improved the tensile, bending, in-plane shear, and bearing characteristics of the prepared composite. The maximum specific tensile, bending, in-plane shear, and bearing strengths are displayed by 3B-2 J-3B, followed by 2B-4 J-2B.