The Decode-Compress-Forward (DCF) is a generalization of Decode-Forward (DF) and Compress-Forward (CF). This paper investigates conditions under which DCF offers gains over DF and CF, addresses the problem of coded modulation for DCF, and evaluates the performance of DCF coded modulation implemented via low-density parity-check (LDPC) codes and polar codes. We begin by revisiting the achievable rate of DCF in discrete memoryless channels under backward decoding. We then study coded modulation for the decode-compress-forward via multi-level coding. We show that the proposed multilevel coding approaches the known achievable rates of DCF. The proposed multilevel coding is implemented (and its performance verified) via a combination of standard DVB-S2 LDPC codes, and polar codes whose design follows the method of Blasco-Serrano.