A tremendous amount of waste black tea bags (BTBs) and date palm surface fibers (DPSFs), at the end of their life cycle, end up in landfills, leading to increased pollution and an increase in the negative impact on the environment. Therefore, this study aims to utilize these normally wasted materials efficiently by developing new composite materials for thermal insulation and sound absorption. Five insulation composite boards were developed, two were bound (BTB or DPSF with polyvinyl Acetate resin (PVA)) and three were hybrids (BTB, DPSF, and resin). In addition, the loose raw waste materials (BTB and DPSF) were tested separately with no binder. Thermal conductivity and sound absorption coefficients were determined for all boards. Thermal stability analysis was reported for the components of the tea bag (string, label, and bag) and one of the composite hybrid boards. Mechanical properties of the boards such as flexural strain, flexural stress, and flexural elastic modulus were determined for the bound and hybrid composites. The results showed that the thermal conductivity coefficients for all the hybrid composite sample boards are less than 0.07 at the ambient temperature of 24 °C and they were enhanced as the BTB ratio was reduced in the hybrid composite boards. The noise reduction coefficient for bound and all hybrid composite samples is greater than 0.37. The composite samples are thermally stable up to 291 °C. Most composite samples have a high flexure modulus between 4.3 MPa and 10.5 MPa. The tea bag raw materials and the composite samples have a low moisture content below 2.25%. These output results seem promising and encouraging using such developed sample boards as eco-friendly thermal insulation and sound absorption and competing with the synthetic ones developed from petrochemicals in building insulation. Moreover, returning these waste materials to circulation and producing new eco-friendly composites can reduce the number of landfills, the level of environmental pollution, and the use of synthetic materials made from fossil resources.