This paper proposes a fully digital post-processing solution for cancelling nonlinear distortion and mirror-frequency interference in wideband direct-conversion receivers (DCRs). Favorable cost, integrability, and power efficiency have made DCRs a popular choice in communication systems. It is also an emerging trend in radar systems since digital post-processing enables sufficient performance. The proposed method cancels the most essential distortion adaptively during normal receiver operation without any prior information. Improved cancellation performance compared to the state-of-the-art is achieved considering inband and neighboring band distortion induced by the strong received signals. This is verified and demonstrated with extensive simulations and true RF hardware measurements.