The escalating demand for high-density storage of hard disk drives has prompted the innovation of advanced technologies to significantly boost an areal density (AD). Among these, three-dimensional magnetic recording systems incorporating double recording layers and bit-patterned magnetic recording (BPMR) have currently emerged as one promising solution. Therefore, this article investigates the integration of double-layer magnetic recording and BPMR technologies which is called double-layer BPMR, aiming for a substantial increase in AD. The primary focus lies on minimizing inter-layer interference and mitigating two-dimensional interferences by optimizing bit-island sizes for both upper and lower layers under the incorporation of staggered-like recording media arrangement and an array of magneto-resistive readers. Moreover, we also employ a rate-5/6 modulation code for compensating these effects. Detailed examinations reveal that our proposed system has a superior bit-error rate performance compared with conventional single-layer BPMR system.