For a Microgrid (MG) with cooling, heating, electricity coordinated supply to satisfy its end customers' multi energy-type demands, a day-ahead coordinated scheduling model is developed. In the model, the objective for achieving the economy of MG owner, and the constraints for the multi-energy supply and demand balances and energy devices characteristics are considered. The fluctuations of solar and wind power generation and electricity load are described by uncertainty intervals. For the nonlinear performance of energy devices, the piecewise linear regression is implemented to make it approximately represented by linear functions, and then the interval linear programming is applied to derive the interval values of the worst- and the best-case optimal solution. Several case studies are given to demonstrate the effectiveness of the proposed method.