In this paper, a novel approach is proposed to jointly recover the transmitted signal and mitigate narrow-band interference (NBI) in OFDM systems using a compressive sensing (CS) framework. NBI degrades the performance of OFDM systems which motivates the need for mitigation techniques to reduce its effect. The main idea behind our approach is to represent the transmitted data and the NBI signal as sparse atoms and then to solve a joint compressive sensing (JCS) problem. The recovery problem is formulated as a weighted optimization problem of two atomic norms and then solved using convex programming. The solution aims to recover the transmitted signal and NBI jointly. The off-grid problem of NBI signal is avoided using the atomic norm. The bit error rate (BER) performance of our proposed JCS recovery approach outperforms the BER performance of the conventional CS-based approach as demonstrated by simulation results.