Model predictive control has proven to be a promising platform for complex systems management and energy efficiency improvement in a large number of applications, particulary prominent in building climate or smart grids control. Interoperation of those systems often turns out to be of a nonlinear nature. The paper proposes a modular coordination mechanism between building zones comfort control and building microgrid energy flows control based on nonlinear model predictive control. The modularity of coordination implies technology separation with interaction through consumption profiles and equivalent prices, where nonlinearity occurs in electricity-heat energy conversion. A method based on sensitivity analysis is exploited and put to parametric formulation to tackle the problem of high computational complexity. The nonlinearity is addressed by choosing the convergence of the local optimum towards the microgrid global optimum in the direction of the lowest cost function values. Iterative approach between zone and microgrid level nonlinear problem finally results in the cost-optimal zone level operation. Results show the ability of the proposed approach to cope with system nonlinearities and illustrate how introduction of a central chiller unit characteristic rises the overall cost benefit of the system.