In this paper, by jointly considering power allocation and network selection, we address the energy efficiency maximization problem in dynamic and heterogeneous wireless networks, where user equipments are typically equipped with multi-homing capability. In order to effectively deal with the dynamics of heterogeneous wireless networks, a stochastic optimization problem is formulated that optimizes the long-term energy efficiency under the constraints of system stability, peak power consumption and average transmission rate. By adopting the parametric approach and Lyapunov optimization, we derive an equivalent optimization problem out of the original problem and then investigate its optimal resource allocation. Then, to reduce the computational complexity, a suboptimal resource allocation algorithm is proposed based on relaxed optimization, which adapts to time-varying channels and stochastic traffic without requiring relevant a priori knowledge. The simulation results demonstrate the theoretical analysis and validate the adaptiveness of our proposed algorithm.