Upper bounds on the bit error rate (BER) for maximum likelihood (ML) decoding are derived in convolutional coded parallel combinatorial spread spectrum (PC/SS) systems over additive white Gaussian noise (AWGN) channels. PC/SS systems can achieve higher data transmission than conventional multicode SS systems. To make the derivation tractable, we put a uniform interleaver between a convolutional encoder and a PC/SS transmitter. Since the PC/SS transmitter is employed as the "inner encoder," the bounds are obtained in a similar manner of the derivation in serially concatenated codes through a uniform interleaver. Two different error patterns in the PC/SS system are considered in the performance analysis. Numerical results show that the derived BER bounds are sufficiently accurate. It is found that the coded PC/SS systems outperform coded all-code-parallel DS/SS systems under the same data rate conditions if the number of pre-assigned PN codes increases.