Structured triacylglycerols play an important role in determining the functional properties of fat-based emulsion products. The aim of the study was to evaluate the physical properties of the emulsion systems manufactured on the basis of enzymatically modified rabbit fat with pumpkin seed oil in the presence ofsn-1,3 regioselective lipase. Emulsions containing variable contents of thickener and variable fat ratios were analyzed for rheological behavior and particle size changes during storage, and their stability was assessed using the Turbiscan test. The results showed that the emulsion containing the majority of rabbit fat and 1 wt% of carboxymethylcellulose was characterized by the highest stability. On the other hand, the emulsions containing higher amounts of pumpkin seed oil in a fatty base characterized the lowest resistance to destabilization processes. The research confirmed the possibility of producing structured fat which can be the basis for new emulsion systems proposed as a food, cosmetic, and pharmaceutical product.