Harmonic/percussive source separation (HPSS) consists in separating the pitched instruments from the percussive parts in a music mixture. In this paper, we propose to apply the recently introduced Masker-Denoiser with twin networks (MaD TwinNet) system to this task. MaD TwinNet is a deep learning architecture that has reached state-of-the-art results in monaural singing voice separation. Herein, we propose to apply it to HPSS by using it to estimate the magnitude spectrogram of the percussive source. Then, we retrieve the complex-valued short-term Fourier transform of the sources by means of a phase recovery algorithm, which minimizes the reconstruction error and enforces the phase of the harmonic part to follow a sinusoidal phase model. Experiments conducted on realistic music mixtures show that this novel separation system outperforms the previous state-of-the art kernel additive model approach.