In this paper, a low probability of intercept (LPI) performance optimization scheme for a joint radar-communications system (JRCS) is proposed, which is able to simultaneously estimate target parameters from the target returns and decode the received communications signals. The primary objective is to improve the LPI performance of a JRCS by optimizing radar waveform design and communications power allocation while guaranteeing a predefined mutual information (MI) threshold for target parameter estimation and a desired communications data rate (CDR) for data transmission, where both traditional isolated sub-band (TISB) and radar isolated sub-band (RISB) situations are discussed. Subsequently, the approach of Lagrange multipliers and the Karush-Kuhn-Tuckers (KKT) optimality conditions are derived to solve the resulting problems. Also, the successive interference cancellation (SIC) technique is employed to obtain the original communications signals free of any radar interference. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed scheme.