Joint radar-communication (JRC) waveform can be used for simultaneous radar detection and communication in the same frequency band. However, radar detection processing requires the prior knowledge of the waveform including the embedded information for matched filtering. To remove this requirement, we propose a unimodular JRC waveform based on composite modulation where the internal modulation embeds information by mapping the bit sequence to different orthogonal signals, and the external modulation performs phase modulation on the internal waveform to satisfy the demand of detection. By adjusting the number of the orthogonal signals, a trade-off between the detection and the communication performance can be made. Besides, a new parameter, dissimilarity, is defined to evaluate the detection performance robustness to unknown embedded information. The numerical results show that the SER performance of the proposed system is similar to that of the multilevel frequency shift keying system, the ambiguity function resembles that of the phase coded signal, and the dissimilarity performance is better than other JRC systems.