Semantic communications (SemComs) have emerged as a promising paradigm for joint data and task-oriented transmissions, combining the demands for both the bit-accurate delivery and end-to-end (E2E) distortion minimization. However, current joint source-channel coding (JSCC) in SemComs is not compatible with the existing communication systems and cannot adapt to the variations of the sources or the channels, while separate source-channel coding (SSCC) is suboptimal in the finite blocklength regime. To address these issues, we propose an adaptive source-channel coding (ASCC) scheme for SemComs over parallel Gaussian channels, where the deep neural network (DNN)-based semantic source coding and conventional digital channel coding are separately deployed and adaptively designed. To enable efficient adaptation between the source and channel coding, we first approximate the E2E data and semantic distortions as functions of source coding rate and bit error ratio (BER) via logistic regression, where BER is further modeled as functions of signal-to-noise ratio (SNR) and channel coding rate. Then, we formulate the weighted sum E2E distortion minimization problem for joint source-channel coding rate and power allocation over parallel channels, which is solved by the successive convex approximation. Finally, simulation results demonstrate that the proposed ASCC scheme outperforms typical deep JSCC and SSCC schemes for both the single- and parallel-channel scenarios while maintaining full compatibility with practical digital systems.