With respect to the probabilistic hesitant fuzzy two-sided matching decision making problems with aspiration levels on criteria, a two-sided matching decision making method based on the regret theory is proposed considering the psychological behaviour of regret aversion of two-sided matching subjects. Firstly, a new Lance distance measure and a Lance score function of the probabilistic hesitant fuzzy element are defined. Then, based on the regret theory, a probabilistic hesitant fuzzy two-sided matching decision making method with aspiration levels on criteria is proposed. In this method, the criterion utility value matrix of two-sided matching subjects are constructed using the expected utility function and the Lance score function of the probabilistic hesitant fuzzy element, the regret-rejoice value matrix of two-sided matching subjects relative to the aspiration levels on criteria are built using the regret-rejoice function, and the perceived value matrix of two-sided matching subjects relative to the aspiration levels on criteria are set up according to the regret theory. Furthermore, an optimization model is constructed using the ideas of maximal deviation method and the new Lance distance measure of the probabilistic hesitant fuzzy element to obtain the weight vectors of the criteria, the comprehensive perceived value matrix of two-sided matching subjects are built using the linear weighted method, and the satisfaction degree matrix of two-sided matching subjects are set up using the range transformation method. Based on these, a multi-objective optimization model is constructed considering maximal satisfaction degree and the stability of two-sided matching alternatives, and the stable two-sided matching outcomes are obtained by solving this model. Finally, an example is given to illustrate the effectiveness and practicability of the proposed two-sided matching decision making method.