Bio-based composites are increasingly used. One of the most frequently used materials is hemp shives, which is agricultural waste. However, as the quantities of this material are lacking, there is a tendency towards finding new and more available materials. Corncob and sawdust are bio by-products that have great potential as insulation materials. In order to use these aggregates, it is necessary to examine their characteristics. New composite materials based on sawdust, corncobs, styrofoam granules, and the mixture of lime and gypsum as the binder were tested in this research. This paper presents the properties of these composites obtained by determining the porosity of samples, volume mass, water absorption, airflow resistance and heat flux, which was followed by the calculation of the thermal conductivity coefficient. Three of the new biocomposite materials, whose samples were 1–5 cm thick for each type of mixture, were investigated. The aim of this research was to analyze the results of different mixtures and sample thicknesses in order to determine the optimum composite material of the proper thickness so that the best possible thermal and sound insulation could be obtained. Based on the conducted analyses, the biocomposite with a thickness of 5 cm, composed of ground corncobs, styrofoam, lime, and gypsum, proved to be the best in terms of thermal and sound insulation. New composite materials can be used as an alternative to conventional materials.