The accelerating interest in energy system models has influenced numerous revolutionized alterations in the wholesale gas and electricity market. This study proposes a novel bi-level multi-follower optimization framework for the strategic behavior observation of an integrated (thermal and electrical) energy service provider (IESP) as a price-maker in the wholesale electricity market (WEM) and natural gas market (NGM). At the upper level, the IESP submits offers/bids in WEM and NGM to procure electricity/gas to the customers. To this end, the IESP endeavors to minimize operational costs and influence the market-clearing price (MCP) by deploying demand-side flexibilities, i.e., elastic electrical and thermal loads. At the lower level, the wholesale electricity market operator (WEMO) and natural gas market operator (NGMO) receive offers/bids from all market participants and clear the market with the goal of maximizing social welfare. The IESP is modelled via the IEEE-33 bus active distribution system (ADS) and an 8 node district heating system (DHS), while the WEM and NGMs are embodied by a 6-bus transmission network (TN) and a 21-node natural gas network (NGN), respectively. Karush–Kuhn–Tucker (KKT) conditions are introduced to transform the multi-follower bi-level optimization problem into a single-level problem, while the inherent nonlinearities of the problem are linearized using the theory of strong duality. Moreover, the intrinsic intermittencies of the renewable energy sources (RES) is dealt with by the risk-averse information gap decision theory (IGDT). The results confirm that flexible electrical and thermal demands can diminish the market-clearing price by as much as 4.1%.