Energy harvesting is considered as a prominent technology, particularly for low-power wireless nodes. In this paper, we propose the use of hybrid energy harvesting (HEH) utilizing multiple type energy sources and present the modeling of HEH communication systems based on their probabilistic natures. According to our approach, received energy levels of an HEH system for possible combinations of energy arrivals are characterized by using Gaussian mixture models, which are used to determine harvested energy levels. The range of harvested energy is partitioned, and probabilities of partitioning intervals are used to form a finite-state Markov energy channel (FSMEC) model as an energy channel. Similar to the energy arrival, we also include the probabilistic energy consumption of wireless node in this model, depending on multiple application services, by means of the FSMEC model. Thus, we develop an integrated Markov energy model for HEH communication systems corresponding to the energy harvesting and energy consumption profiles. To evaluate the performance of an HEH communication system, we derive the expressions of energy outage, energy shortage, and service loss probabilities analytically. In numerical studies, the derived expressions are verified by matching simulation results, and it is shown that the performance improves significantly with energy source diversity.