Spectral sub-bands do not portray the same perceptual relevance. In audio coding, it is therefore desirable to have independent control over each of the constituent bands so that bitrate assignment and signal reconstruction can be achieved efficiently. In this work, we present a novel neural audio coding network that natively supports a multi-band coding paradigm. Our model extends the idea of compressed skip connections in the U-Net-based codec, allowing for independent control over both core and high band-specific reconstructions and bit allocation. Our system reconstructs the full-band signal mainly from the condensed core-band code, therefore exploiting and showcasing its bandwidth extension capabilities to its fullest. Meanwhile, the low-bitrate high-band code helps the high-band reconstruction similarly to MPEG audio codecs' spectral bandwidth replication. MUSHRA tests show that the proposed model not only improves the quality of the core band by explicitly assigning more bits to it but retains a good quality in the high-band as well.