To economically dispatch distributed energy resources (DERs) while addressing operational concerns of the electric grid, distribution locational marginal price (DLMP)-based market frameworks have been formulated for the electric distribution grid. This paper proposes to extend this methodology to thermal grids, i.e. district heating or cooling systems, and presents a market-clearing mechanism based on the alternating direction method of multipliers (ADMM) for coordinating between thermal grid, electric grid and DER operation. The ability of the proposed mechanism to achieve the market equilibrium for a combined thermal and electric grid is demonstrated for a test case with 22 flexible loads (FLs).